Step 1: Reaction of benzene diazonium chloride with water.
Benzene diazonium chloride gives phenol when warmed with water.
\[
\mathrm{C_6H_5N_2^+Cl^- + H_2O \xrightarrow{\Delta} C_6H_5OH + N_2 + HCl}
\]
Step 2: Identifying the compound formed.
The compound formed is phenol.
\[
\mathrm{C_6H_5OH}
\]
Step 3: Formation of sodium salt of phenol.
Phenol reacts with sodium hydroxide to form sodium phenoxide.
\[
\mathrm{C_6H_5OH + NaOH \rightarrow C_6H_5ONa + H_2O}
\]
Step 4: Reaction of sodium phenoxide with allyl bromide.
Sodium phenoxide reacts with allyl bromide through Williamson ether synthesis.
\[
\mathrm{C_6H_5ONa + BrCH_2CH=CH_2 \rightarrow C_6H_5OCH_2CH=CH_2 + NaBr}
\]
Step 5: Identifying the product [X].
The product formed is allyl phenyl ether.
\[
\mathrm{C_6H_5-O-CH_2-CH=CH_2}
\]
Step 6: Matching with the options.
Option (B) represents:
\[
\mathrm{C_6H_5-O-CH_2-CH=CH_2}
\]
This is exactly allyl phenyl ether.
Step 7: Final conclusion.
Thus, compound [X] is allyl phenyl ether.
\[
\boxed{\mathrm{C_6H_5-O-CH_2-CH=CH_2}}
\]
Hence, the correct answer is option (B).