Carbanions are usually sp³ hybridized. Free radical carbons, carbocations, and double bonded carbons are all sp² hybridized.

The bond in question is a double bond, and thus is composed of one sigma and one pi bond.

Benzylamine consists of a benzene ring with a -CH₂NH₂ substituent. The benzene ring contains three double bonds, and the substituent has none.

Each bond in a compound represents a sigma bond. Each additional bond represents a pi bond; thus, double binds result from one sigma and one pi bond, and triple bonds from one sigma and two pi bonds. In benzylamine, there are three double bonds and seventeen total bonds, three of which are double bonds. The compound will have a total of seventeen sigma bonds and three pi bonds.

Recall the formula for degrees of unsaturation as the sum of the number of pi bonds and the number of rings. This value is equivalent to the below formula.

C is the number of carbons, H is the number of hydrogens, X is the number of halogens, and N is the number of nitrogens. Using this formula, compound A has four degrees of unsaturation, while the product only has two.

The reaction described is a hydrogenation reaction, which will reduce double bonds. The reaction saturates two pi bonds of compound A, meaning the remaining degrees of unsaturation in that compound have to come from two rings. Essentially, due to the reaction given, we know that the product contains no double bonds but still has two degrees of unsaturation. These unsaturation points must correspond to rings.

The molecule has four single bonds and one double bond.

The first carbon forms two single bonds with the two hydrogen atoms, and a double bond to the second carbon. The second carbon has single bonds with the third hydrogen and the chlorine atom. In total, each carbon has two single bonds and one double bond (to each other), for a total of four single bonds and one double bond.

Each single bond contains one sigma bond and zero pi bonds. Each double bond contains one sigma bond and one pi bond. This molecule has five sigma bonds, and one pi bond. 

A degree of unsaturation results from either a ring or a double bond. In the case of a benzene ring or phenyl substituent, four degrees of unsaturation are present: the ring itself and the three included double bonds.

Compounds A, B, and C all possess a benzene ring, but compounds A and C also have one additional degree of unsaturation. Compound A contains a carbon-oxygen double bond in the ketone group and compound C contains a carbon-carbon double bond in the alkene group. In addition to the four degrees from the ring, these additions bring their total degrees of unsaturation to five. Compound B has no additional double bond, and therefore has four degrees of unsaturation.

The degree of unsaturation is equal to the number of rings plus the number of pi bonds in a molecule. Ephedrine has one ring and three pi bonds, so its degree of unsaturation is four.

To arrive at this answer, one could also use the formula below, where  is the number of carbon atoms,  is the number of hydrogen atoms,  is the number of halogen atoms, and  is the number of nitrogen atoms.

 For ephedrine, , , , and .

For a compound to be considered aromatic, it must be flat, cyclic, and conjugated and it must obey Huckel's rule. Huckel's rule states that an aromatic compound must have  pi electrons in the overlapping p orbitals in order to be aromatic (n in this formula represents any integer). Only compounds with 2, 6, 10, 14, . . .  pi electrons can be considered aromatic. Compound A has 6 pi electrons, compound B has 4, and compound C has 8. This eliminates answers B and C. Answer D is not cyclic, and therefore cannot be aromatic. The only aromatic compound is answer choice A, which you should recognize as benzene.

Acetic acid has the formula . This compound is common enough that the IUPAC name will rarely be given, and you will need to recognize it by common name alone.

Whenever two atoms are directly bonded to one another, a -bond is formed. Even when there is a double or triple bond between two atoms, there is still one -bond between the two atoms. In acetic acid, there are seven bonds between atoms. Even though the carbonyl carbon has a double bond, there is still a -bond between the carbon and oxygen. As a result, there are seven total -bonds in a molecule of acetic acid.

The carbon at the center of a carbonyl group bonds with three sigma bonds, and one pi bond. The pi bond exists above and below the plane of the sigma bond. This carbon thus shows sp2 hybridization.