= Solution
Number the OH-bearing <carbon> C1 and the adjacent brominated <carbon> C2. In the trans <bromohydrin>, <base (chemistry)> generates an <alkoxide>. A <chair conformation> can place O at C1 and Br at C2 trans-diaxial, aligning the <oxygen> <nucleophile> for <backside attack> at C2. Intramolecular SN2 closure expels <bromide> and inverts C2: \b[the retained C1–O bond and the newly formed C2–O bond are both on the original OH face], giving the <epoxide> shown. <ring inversion> can provide the reactive chair even if it is not the dominant ground-state conformer.
The cis <bromohydrin> cannot place OH and Br trans-diaxial: one is axial when the other is equatorial. In the chair with Br axial, the <hydrogen> on C1 can instead be antiperiplanar to C2–Br. An <alkoxide>-assisted semipinacol pathway moves the C1–H <bonding pair> to C2 while the <oxygen> <lone pair> forms C1=O and <bromide> departs. \b[<hydride> migration gives the <ketone> without changing the <carbon> skeleton.] The <hydrogen> is transferred to C2 rather than expelled as a free <hydride>. The original phenyl-bearing stereocentre is not involved in either bond-reorganization sequence. Configuration controls which properly aligned displacement or migration can occur; a flat ring drawing alone conceals that distinction.
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