Step 1: Understanding the Concept:
S\(_N\)2 reactions are favored by polar aprotic solvents. These solvents solvate the cation but not the anion, leaving the nucleophile highly reactive.
Step 2: Detailed Explanation:
\begin{itemize}
\item CH\(_3\)OH and H\(_2\)O are polar protic solvents. They solvate the nucleophile through hydrogen bonding, reducing its nucleophilicity and thus slowing the S\(_N\)2 reaction.
\item DMSO (dimethyl sulfoxide) is a polar aprotic solvent. It solvates the cation but not the anion, leaving the nucleophile "naked" and highly reactive, maximizing the S\(_N\)2 rate.
\item Benzene is non-polar and does not stabilize the charged transition state, so the reaction is very slow.
\end{itemize}
Step 3: Final Answer:
The rate of S\(_N\)2 reaction is maximum in DMSO, option (C).