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(C) $1$. The starting material is $2$-hydroxymethylcyclohexanol. Treatment with excess $PCC$ oxidizes both the secondary alcohol to a ketone and the p

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(C) $1$. The starting material is $2$-hydroxymethylcyclohexanol. Treatment with excess $PCC$ oxidizes both the secondary alcohol to a ketone and the primary alcohol to an aldehyde,yielding $2$-formylcyclohexanone.$2$. Treatment with $1$ equivalent of ethylene glycol in the presence of $H^+$ selectively protects the more reactive aldehyde group as a cyclic acetal.$3$. Reaction with $CH_3MgBr$ followed by $H_3O^+$ adds a methyl group to the ketone carbonyl,forming a tertiary alcohol,and simultaneously deprotects the acetal back to the aldehyde.$4$. Finally,$NaBH_4$ reduces the aldehyde group to a primary alcohol,resulting in $1$-methyl-$2$-hydroxymethylcyclohexanol.

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