Step 1: Formation of \(X\).
Propene reacts with HBr in the presence of peroxide.
This follows the anti-Markovnikov addition (Kharasch effect).
\[
CH_3CH=CH_2
\xrightarrow[\text{Peroxide}]{HBr}
CH_3CH_2CH_2Br
\]
Thus,
\[
\boxed{X=n\text{-propyl bromide}}
\]
Step 2: Formation of \(Y\).
\(n\)-Propyl bromide undergoes Friedel--Crafts alkylation with benzene.
The initially formed primary carbocation rearranges to the more stable secondary carbocation.
\[
C_6H_6 + CH_3CH_2CH_2Br
\xrightarrow{AlCl_3}
C_6H_5CH(CH_3)_2
\]
Hence,
\[
\boxed{Y=\text{Cumene (isopropylbenzene)}}
\]
Step 3: Oxidation of cumene.
Any alkyl benzene having at least one benzylic hydrogen is oxidized by alkaline \(KMnO_4\) to benzoic acid.
\[
C_6H_5CH(CH_3)_2
\xrightarrow{KMnO_4}
C_6H_5COOH
\]
After acidification,
\[
\boxed{\text{Benzoic acid is formed}}
\]
Step 4: Soda-lime decarboxylation.
Benzoic acid forms sodium benzoate, which on heating with soda lime undergoes decarboxylation.
\[
C_6H_5COONa
\xrightarrow[\Delta]{NaOH/CaO}
C_6H_6
\]
Therefore,
\[
\boxed{Z=\text{Benzene}}
\]
Final Answer:
\[
\boxed{\text{Benzene}}
\]
\[
\boxed{\text{Answer = (C)}}
\]