This is a Grignard reagent carbon-carbon bond forming reaction. This reaction is being used with an ester which goes through a ketone intermediate with requires a second attack form the organolithium to reduce to an alcohol. Esters and acyl chlorides go to an alcohol with two of the same R groups from the organolithium in a Grignard reaction. This structure fits the bill:

LiAlH4 is a very strong reducing agent and it is a reactant that can reduce acyl chlorides into alcohols. There are 2 alcohols to choose from and now it needs to be known that LiAlH4 doesn't add anything but hydrogens to its substrate. (Note that in the correct answer, there is another H that is not drawn on the carbon bearing the hydroxyl group).

Below is the mechanism for the reaction given which is called the McMurry Reaction. It is a titanium (Ti) prompted pinacol coupling followed by deoxygenation.

This reaction involves the generation of a radical by single electron transfer that couple through carbon-carbon bond formation to form the product pinacol. This reaction as shown below occurs in an aprotic solvlent:

Below is the mechanism for the reaction given which is called the McMurry Reaction. It is a titanium (Ti) prompted pinacol coupling followed by deoxygenation.

Alkyl lithium (organolithium) reagents are powerful reducing agents and react much in the same manner as Grignard reagents through the formation of a carbanion. In the first step of the reaction, the carbanion attacks at the carbonyl, creating a charged intermediate, which is neutralized by reformation of the carbonyl and the release of ethoxide (the ester chain is the leaving group). However, the alkyl lithium reagent continues the reaction by attacking at the carbonyl once again. This time, there is no suitable leaving group (every group bound is a carbon chain) and the intermediate remains until a proton transfer is facilitated to neutralize the oxygen's charge.

To answer this question, it's important to consider what types of molecules are reacting. The pentanoic acid is a carboxylic acid, and the butanol is an alcohol. When carboxylic acids are reacted with alcohols in the presence of an acid catalyst, the result is an ester. 

This is a basic Claisen condensation reaction in which the  functions to take off the acidic hydrogen (between the ketone and the ester) and then the same molecule can attack a carbonyl carbon to yield .

The attack at the ester carbonyl leads to the leaving of  group.

Treatment of ethyl acetate with methoxide will yield the enolate ion (II). However, side trans-esterification reactions will also result in formation of product III.

It is extremely useful in organic synthesis to utilize methods by which less reactive carboxylic acids (and their derivatives) may be converted to more reactive species, like acid chlorides. Such reactions are not always intuitive as they proceed by transforming low-energy species to more energetic states. Reagents such as thionyl chloride  and phosphorus tribromide , which you have likely seen previously in examination of common alcohol reactions, readily convert carboxylic acids to acid chlorides. The reaction is energetically favorable due to the formation of sulfur dioxide, a very stable gas.