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(A) The starting material is a dihydroxy compound containing both a phenolic $-OH$ group and an aliphatic $-OH$ group. Phenolic $-OH$ is more acidic t

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(A) The starting material is a dihydroxy compound containing both a phenolic $-OH$ group and an aliphatic $-OH$ group. Phenolic $-OH$ is more acidic than aliphatic $-OH$ due to the resonance stabilization of the phenoxide ion. When one equivalent of $NaOH$ is added,it selectively deprotonates the more acidic phenolic $-OH$ group to form a phenoxide ion. Subsequent reaction with $CH_3Br$ proceeds via an $S_N2$ mechanism,where the phenoxide oxygen acts as a nucleophile and attacks the methyl bromide,resulting in the formation of a methoxy group at the phenolic position while the aliphatic $-OH$ group remains unaffected. Thus,the product $(A)$ is the structure with a methoxy group at the phenolic position.

Product $(A)$ is

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