Step 1: Identify the alkyne \(X\).
Given:
\[
X(C_4H_6)
\]
does not form sodium alkynide.
Only terminal alkynes possess acidic hydrogen and form sodium alkynides.
Therefore \(X\) must be an internal alkyne.
Among \(C_4H_6\) alkynes,
\[
CH_3CH_2C\equiv CH
\]
(1-butyne) is terminal,
while
\[
CH_3C\equiv CCH_3
\]
(2-butyne) is internal.
Hence,
\[
\boxed{X=2\text{-butyne}}
\]
Step 2: Reaction of \(X\) with HBr.
Addition of two moles of HBr to an alkyne gives a geminal dibromide.
\[
CH_3C\equiv CCH_3
\xrightarrow[2\,HBr]{}
CH_3CBr_2CH_2CH_3
\]
Thus,
\[
\boxed{Y=\text{geminal dibromide}}
\]
Step 3: Reaction of \(X\) with \(Na/\text{liq. }NH_3\).
Dissolving metal reduction converts an alkyne into a trans-alkene.
\[
CH_3C\equiv CCH_3
\xrightarrow{Na/NH_3}
trans\text{-}CH_3CH=CHCH_3
\]
which is trans-2-butene.
Since the dipole moments cancel,
\[
\mu=0.
\]
Therefore,
\[
\boxed{Z=\text{non-polar compound}}
\]
Final Answer:
\[
\boxed{Y=\text{geminal dibromide}}
\]
\[
\boxed{Z=\text{non-polar compound}}
\]
\[
\boxed{\text{Answer = (A)}}
\]