Requirement from the product. The product \(P\) is a tertiary benzylic alcohol of the form Ph–C(OH)(CH\(_3\))\(_2\). Therefore, after adding CH\(_3^-\) (from CH\(_3\)MgBr) and protonation, the carbonyl precursor must deliver a central carbon attached to Ph and two CH\(_3\) groups.
Functional groups that work.
• Aryl methyl ketone (acetophenone type): Ph–CO–CH\(_3\) \(\xrightarrow{\;\text{CH}_3\text{MgBr}\;}\) Ph–C(OMgBr)(CH\(_3\))\(_2\) \(\xrightarrow{\;\text{H}_3\text{O}^+\;}\) Ph–C(OH)(CH\(_3\))\(_2\) \(\Rightarrow\) matches \(P\) \(\Rightarrow\) (B) correct.
• Acyl derivatives that convert to that ketone then add again (e.g., acid chloride of benzoic acid): first addition gives acetophenone, a second methyl addition occurs under standard conditions, affording the same tertiary alcohol on work-up \(\Rightarrow\) (C) correct.
Why the others are not suitable.
Options that are aldehydes (Ph–CHO) give only a secondary alcohol (Ph–CH(OH)–CH\(_3\)), not tertiary. Esters/ether-like variants that would place an extra –OR group on the benzylic carbon either require different stoichiometry or give a different carbon skeleton than \(P\). Hence (A) and (D) do not furnish \(P\) as the major product under the given conditions.