Compound X undergoes following sequence of reactions to give the Lactone Y.

Aldol Addition: Isobutyraldehyde reacts with Formaldehyde in the presence of KOH. Since Isobutyraldehyde has only one alpha-hydrogen, it adds one HCHO unit to form 2,2-dimethyl-3-hydroxypropanal.

(CH3)2CHCHO + HCHO  ->  HO-CH2-C(CH3)2-CHO

2. Cyanohydrin Formation: The aldehyde group reacts with $KCN$ to form a cyanohydrin.

$$HO-CH_2-C(CH_3)_2-CHO -> HO-CH2-C(CH3)2-CH(OH)CN

3. Hydrolysis & Cyclization: Acidic hydrolysis  converts the $-CN$ to $-COOH$. The gamma-hydroxy group then attacks the carboxylic acid to form the stable 5-membered Lactone (Y).