'A' and 'B' in the above reaction are :  

The starting material is a 2-alkylcyclohexanone (a cyclic ketone with an alkyl group $$R$$ at the $$\alpha$$-position).

When treated with a strong oxidizing agent like $$\text{KMnO}_4$$, cyclic ketones undergo oxidative cleavage of the $$\text{C}-\text{C}$$ bond adjacent to the carbonyl group.

Regioselectivity: The bond cleavage preferentially occurs between the carbonyl carbon ($$\text{C}_1$$) and the more substituted $$\alpha$$-carbon ($$\text{C}_2$$, which bears the alkyl group $$R$$).

The carbonyl carbon ($$\text{C}_1$$) is oxidized to a carboxylic acid ($$-\text{CO}_2\text{H}$$), and the substituted $$\alpha$$-carbon ($$\text{C}_2$$) is oxidized to a ketone ($$-\text{C}(=\text{O})R$$) group because it holds the alkyl chain.

Thus, the ring opens up to form a keto-acid.

Product 'A' is then treated with hydrazine and a strong base ($$\text{NH}_2\text{NH}_2, \text{KOH}$$) followed by acidic workup ($$\text{H}_3\text{O}^+$$). This reagent combination describes a Wolff-Kishner Reduction.

The Wolff-Kishner reduction selectively converts carbonyl groups ($$\text{C}=\text{O}$$) of aldehydes and ketones into methylene groups ($$\text{CH}_2$$).

Selectivity: It does not reduce carboxylic acid ($$-\text{CO}_2\text{H}$$) groups.

The ketone carbonyl group ($$\text{C}=\text{O}$$) attached to $$R$$ is completely reduced to a $$-\text{CH}_2-$$ group.

Correct Option B.