Step 1: Identify the reaction type.
The reagent hydrazine \((NH_2NH_2)\) in presence of \(KOH\) and glycol indicates the Wolff–Kishner reduction.
This reaction is used to reduce carbonyl compounds (aldehydes or ketones) to alkanes.
Step 2: Understand the transformation in compound \([X]\).
Compound \([X]\) contains a carbonyl group \((C=O)\).
Under Wolff–Kishner conditions, this carbonyl group is removed and replaced by a methylene group \((-CH_2-)\).
Step 3: Write the general reaction.
\[
R-CO-R' \xrightarrow{NH_2NH_2, \, KOH, \, glycol} R-CH_2-R'
\]
Thus, the carbonyl group is completely reduced.
Step 4: Formation of product \([Y]\).
In the given reaction, the \(C=O\) group in compound \([X]\) is converted into \(-CH_2-\).
All other substituents such as halogen remain unaffected.
Therefore, the structure of \([Y]\) matches the reduced form of \([X]\).
Step 5: Evaluate the Assertion (A).
The assertion states that compound \([X]\) reacts with hydrazine in presence of \(KOH/glycol\) to form \([Y]\).
This is correct because it represents Wolff–Kishner reduction.
Step 6: Evaluate the Reason (R).
The reason states that reduction occurs and carbonyl group is reduced to methylene group.
This is exactly the principle of Wolff–Kishner reduction.
Thus, the reason correctly explains the assertion.
Final Answer:
The correct option is:
\[
\boxed{\text{(B) Both A and R are correct and R is the correct explanation of A}}
\]