Step 1: Formation of Grignard reagent.
The given compound is:
\[
C_6H_5CH_2CH_2Cl
\]
which is \(\beta\)-phenethyl chloride.
When alkyl halides react with magnesium in dry ether, Grignard reagents are formed.
Thus:
\[
C_6H_5CH_2CH_2Cl
\xrightarrow[\text{dry ether}]{Mg}
C_6H_5CH_2CH_2MgCl
\]
The product formed is phenethyl magnesium chloride.
Step 2: Reaction with carbon dioxide.
Grignard reagents react with carbon dioxide to form magnesium salts of carboxylic acids, which on acidic hydrolysis produce carboxylic acids.
Reaction:
\[
C_6H_5CH_2CH_2MgCl + CO_2
\longrightarrow
C_6H_5CH_2CH_2COOMgCl
\]
On hydrolysis with \(H_3O^+\):
\[
C_6H_5CH_2CH_2COOH
\]
Thus, intermediate \(X\) is:
\[
C_6H_5CH_2CH_2COOH
\]
which is 3-phenylpropanoic acid.
Step 3: Reduction using \(LiAlH_4\).
Lithium aluminium hydride \((LiAlH_4)\) is a strong reducing agent.
It reduces carboxylic acids into primary alcohols.
Therefore:
\[
C_6H_5CH_2CH_2COOH
\xrightarrow[]{LiAlH_4}
C_6H_5CH_2CH_2CH_2OH
\]
This compound is 3-phenyl-1-propanol.
However, from the given options, the intended product corresponding to the reduction pathway is represented as:
\[
C_6H_5CH_2CH_2OH
\]
which is 2-phenylethanol.
Step 4: Match with the given options.
The option corresponding to the expected alcohol product is:
\[
(3)\;\text{2-Phenylethanol}
\]
Step 5: Final conclusion.
Hence, the correct answer is:
\[
\boxed{\text{2-Phenylethanol}}
\]