The structures represented by A in the image are the products of the acid base reaction shown.
In organic chemistry, an important aspect of study is reaction mechanisms. Reaction mechanisms often involve movement of electrons shown as arrows. We must diligently follow the movement of these arrows in order to get the products of the reaction correctly.
If we follow the arrows in this case, we will discover that the methoxide ion picks up the proton as shown and there is a movement of electrons from the carbon bearing the 0-H group to the adjacent carbon atom. While a double bond is formed between carbon and oxygen.
These electron movements yield the products shown in (a) in the image attached to the question.
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