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

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(B) $(1)$ 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, which corresponds to option $(B)$.

The product $(D)$ will be

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