The answer is A.
3-bromo-3-methylhexane is a tertiary halogenoalkane, so it is hydrolysed by the \(\text{S}_\text{N}1\) mechanism. The C-Br bond breaks heterolytically in the slow step to give a tertiary carbocation, stabilised by the three electron-donating alkyl groups (and backside attack is hindered by these bulky groups). The carbocation is then attacked by a nucleophile (\(\text{H}_2\text{O}\) or \(\text{OH}^-\)).
The carbocation is trigonal planar, so the nucleophile can attack from either face with equal chance. Because C3 of the product, 3-methylhexan-3-ol, carries four different groups (OH, methyl, ethyl and propyl), the two modes of attack give a racemic mixture of the two enantiomers: the two isomeric alcohols.
• B is wrong: a carbocation is electron-deficient; it is attacked by an electron-pair donor (a nucleophile), not an electrophile.
• C is wrong: attack by a nucleophile on a slightly positive carbon in one step is the \(\text{S}_\text{N}2\) mechanism, which is blocked at this hindered tertiary carbon; here the C-Br bond first breaks to give a carbocation, and it is the carbocation that the nucleophile attacks.
• D is wrong: a slightly positive carbon attracts nucleophiles, not electrophiles, and no electrophile is involved in hydrolysis.
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