The molecule's longest carbon chain has 6 carbons (thus, "hex-"), and the lack of double bonds makes it an alkane (thus "hexane"). The longest chain is a ring structure (thus "cyclohexane"), and the one branching group is a carbon chain consisting of one carbon and no double bonds (a "methyl" group). Because there are no other functional groups on the molecule there is no need to put a number before the location of the methyl group (thus "methylcyclohexane").

The molecule's longest carbon chain has 5 carbons (thus, "pent"), and the lack of double bonds makes it an alkane (thus "pentane"). The one functional group is a bromine atom attached to carbon number 3 (whether read from left to right or right to left, the bromine is always on carbon number 3). Thus, the molecule is named "3-bromopentane."

The molecule's longest carbon chain has 5 carbons (thus, "pent-"), and the carbon-carbon double bond makes it an alkENE (thus "pentene"). The location of the double bond must be specified, and numbering the carbon chain to give the double bond the lowest numbers possible mean that it is numbered from right to left, putting the double bond between carbon 2 and carbon 3. This will put the methyl group on carbon 3. 

Regarding stereochemistry, on carbon 2, the higher priority substituent is the methyl group. On carbon 3, the ethyl group is the higher priority. The higher priority substituents are on the same side of the double bond, and therefore the stereochemistry designation is "Z."

The molecule's longest carbon chain has 6 carbons (thus, "hex-"), and the lack of carbon-carbon double bonds makes it an alkANE (thus "hexan-"). The presence of a hydroxyl group makes this molecule an alcohol (thus "hexanol"). The longest carbon chain is a ring structure (thus "cyclohexanol"), and the location of the alcohol group is assumed to be carbon 1 because it's the highest priority functional group on the molecule. The only other substituent is a methyl group, and numbering the carbon chain starting from the one containing the alcohol group and moving toward the methyl group puts the methyl group on carbon 2. Thus "2-methylcyclohexanol."

The molecule's longest carbon chain has 6 carbons (thus, "hex-"), and the presence of three double bonds makes it an alkENE, more specifically, a triene (thus "hexatriene"). Because there is more than one way in which the double bonds can be arranged it's important to place locants indicating the lower-numbered carbon in each double bond (1, 3, and 5 in this case).

The longest carbon chain is  carbons long (thus ""), and the double bond makes it an alkene (thus ""). The highest priority functional group is the double bond, and the carbon chain must be numbered such that this functional group is given the lowest number carbon. Counting from left to right puts the double bond between carbons  and , which is lower than counting from right to left , therefore the numbering goes from left to right, and the molecule is thus a "." The substituents are a bromine on carbon   and a chlorine on carbon  . IUPAC rules state that the substituents are listed in alphabetical order when naming (thus "").

Finally, stereochemistry must be taken into account. On carbon , the bromine is of higher priority than the methyl group (when taking atomic number into account, per the Cahn-Ingold-Prelog rules), and is located "above" the double bond. On carbon , the chlorine group is higher priority, and is located "below" the double bond. Because the higher priority groups are across the double bond from each other, the molecule is given the "E" designation.

When naming an organic compound by the IUPAC rules, it's best to first start by identifying the functional groups present.

In this particular case we have:

An Ester in the middle as shown here:

a Methyl group shown here: 

and a Butyl group attached to the ester:

Next, we should identify what functional group has the highest priority, as that will form the base name of the compound:

According to IUPAC convention, Carboxylic Acid derivatives including Esters have the highest priority then carbonyls then alcohols, amines, alkenes, alkynes, and alkanes, so in this case the Ester group has the highest priority and therefore makes up the name of the base compound.

Next, we want to number the longest carbon chain with the highest priority functional group with the lowest number. In this case this means we want the carbonyl of the ester to be carbon number #1, so let's start there and number the carbon chain.

You should get something like this:

Notice there are two sixes. The reason why is because there are two possible pathways for the carbon numbering to continue, but both are equivalent meaning no matter what we do there is a 5-methyl group and the carbon chain is 6 carbons long.

Now that we have numbered the carbon chain we can begin our naming.

Let's start with the base name:

According to IUPAC convention the base name for an ester compound is -oate, so in this case we have a hexanoate, which can also be written as hexan-1-oate, but this isn't needed as it as the ester is at carbon 1.

We also have a methyl group at the 5-carbon so in this gives us:

5-methylhexanoate.

However, we aren't done as we haven't named the substituent on the other side of the ester. Let's first count the number of carbons it has. Since this chain has 4 carbons it is a butyl group, as according to IUPAC the chain on the side farthest from carbonyl carbon of the ester is named as a substituent and placed in front of the name of the compound.

This makes our final answer Butyl 5-methylhexanoate.

Now let's go over the other answer choices and why they are wrong:

1) Butyl 5-methylhexenoate is almost correct except for the fact it says Butyl 5-methylhexenoate. The "en" indicates there is an alkene (double bond) in the compound, and since there isn't this can't be the right answer.

2) Butyl 2-methylhex-6-anoate is wrong because the ester group isn't assigned the highest priority. In IUPAC nomenclature you want to assign the highest priority functional group the lowest number possible in the carbon chain.

3) Butyl 2-methylhex-6-enoate is wrong for a mix of the reasons in the previous 2 answers. It says Butyl 2-methylhex-6-enoate in it, and the compound doesn't have an alkene. It also makes the mistake of not making the ester group (the highest priority functional group) have the lowest number possible in the carbon chain, so this can't be right either.

4) 1-butoxy-5-methylhexanone is wrong because it interprets the ester as being a ketone and an ether group instead of an ester.

When naming an organic compound by the IUPAC, it's best to first start by identifying the functional groups present.

In this particular case we have:

A carboxylic acid shown here:

An alkene in the middle of the carbon chain:

A methyl group:

and a ketone towards the end:

Next, we should identify what functional group has the highest priority, as that will form the base name of the compound:

According to IUPAC convention, Carboxylic Acid derivatives including Esters have the highest priority then carbonyls (in this case the ketone) then alcohols, amines, alkenes, alkynes, and alkanes, so in this case the Ester group has the highest priority and therefore makes up the name of the base compound.

Next, we want to number the longest carbon chain with the highest priority functional group with the lowest number. In this case this means we want the carbonyl of the carboxylic acid to be carbon number #1, so let's start there and number the carbon chain.

You should get something like this:

Now that we have numbered the carbon chain we can begin our naming.

Let's start with the base name:

According to IUPAC convention the base name for an carboxylic acid compound is -oic acid, so in this case we have a decanoic acid, which can also be written as decan-1-oic acid, but this isn't needed as it as the carboxylic acid is at carbon 1.

Next notice that we have an alkene that's part of the main chain, since it is part of the main chain we include it in the base name, so we must change our name from decanoic acid to dec-4-enoic acid because the lowest it can be numbered is #4, however since the highest priority groups on the alkene are facing opposite to each other it is an E (Entgegen) alkene, so we can name it (4E)-decenoic acid

We also have a methyl group at carbon 5. This gives us:

(4E)-5-methyldecenoic acid.

Finally we have a ketone as a substituent, and a ketone as a substituent is called an oxo, so it becomes 9-oxo.

Now we must order our substituents alphabetically. Thus it becomes

(4E)-5-methyl-9-oxodecenoic acid which is our final answer.

Now let's go over the wrong answers:

1) (4E)-9-oxo-5-methyldecenoic acid is wrong because the substituents aren't ordered alphabetically.

2) 5-methyl-9-oxodecanoic acid is wrong because it says decanoic acid when there is an alkene present.

3) 9-oxo-5-methyldecanoic acid is wrong because it says decanoic acid when there is an alkene present, and because the substituents aren't ordered alphabetically.

4) 10-carboxy-5-methyldecan-2-one is wrong because the carboxylic acid group isn't highest priority and it omits the alkene in this compound.

The carbon chain is  carbons long (thus ""), and the presence of a double and triple bond make it necessary to put both the "" suffix (to designate the double bond) and the "" suffix (to designate the triple bond) in the name of the molecule. The carbon chain is numbered from left to right, putting the alkyne and alkene functionalities between carbons  and , respectively. To reduce ambiguity when there are multiple multiple bonds, it's advisable to put the locand of the multiple bond directly before the suffixes, rather than before the parent chain. When ordering the multiple bonds in the name of the molecule, the alkene suffix comes before the alkyne suffix, and the final "" in the suffix "" is dropped. Thus, the molecule is "."

Finally, stereochemistry must be taken into account. On carbon , the carbon chain is of higher priority than the implied hydrogen (when taking atomic number into account, per the Cahn-Ingold-Prelog rules), and is located "above" the double bond. On carbon , the alkyl group is higher priority, and is located "below" the double bond. Because the higher priority groups are across the double bond from each other, the molecule is given the "E" designation.

The longest carbon chain is  carbons long (thus ""), and the double bond makes it an alkene (thus ""). The highest priority functional group is the double bond, and the carbon chain must be numbered such that this functional group is given the lowest number carbon. Counting from either direction puts the double bond between carbons  and the molecule is thus a "." The substituents are a bromine on carbon  when counting from right to left, and  from left to right. The carbon chain is numbered so substituents are given the lowest numbers possible. Thus, the carbon chain is numbered from right to left, and the molecule is .

Finally, stereochemistry must be taken into account. On carbon , the carbon chain is of higher priority than the implied hydrogen (when taking atomic number into account, per the Cahn-Ingold-Prelog rules), and is located "below" the double bond. On carbon , the alkyl group is higher priority, and is located "above" the double bond. Because the higher priority groups are across the double bond from each other, the molecule is given the "E" designation.