Step 1: Formation of alkyne intermediate \(X\).
The given compound is a vicinal dibromide. On treatment with excess sodium amide (\(\text{NaNH}_2\)), double dehydrohalogenation occurs, leading to the formation of a terminal alkyne \(X\).
Step 2: Formation of acetylide ion.
The terminal alkyne reacts with \(\text{NaNH}_2\) to form a sodium acetylide ion due to the acidic nature of the terminal hydrogen.
Step 3: Alkylation of acetylide ion.
The acetylide ion undergoes nucleophilic substitution with isopropyl bromide, resulting in carbon–carbon bond formation and chain extension.
Step 4: Identify the final product.
The alkylation introduces an isopropyl group at the terminal carbon of the alkyne, giving the final product:
\[
\text{5-methylhex-2-yne}
\]
Final Answer:
\[
\boxed{\text{5-methylhex-2-yne}}
\]