Identify (X) and (Y) in the following transformation :

This question is built on drawn structures, so the options cannot be reproduced as text. The chemistry behind the official answer is outlined below.
The sequence is organotin chemistry on a dibutylstannylene fragment. LDA is a strong, bulky, non-nucleophilic amide base: its role is to deprotonate rather than to add, generating a carbanionic centre alpha to tin in intermediate (X).
The second step uses CH2Cl2 with MeLi. MeLi deprotonates dichloromethane to give the chloromethyllithium carbenoid LiCHCl2/ClCH2Li, a classic one-carbon homologating reagent. Reaction of a carbenoid with the organotin intermediate inserts a CH2 unit, so (Y) is the ring-expanded or homologated stannacycle rather than a free stannylene.
The key discrimination among the options is that a genuine tin-carbon double bond, written Sn=CH2, is not the product here: stannenes of that type are extremely reactive and are not isolated under these simple conditions, so options depicting Sn=CH2 for both X and Y do not describe the real transformation.
Per the official final answer key the answer is option (A).
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