= Solution
The <alcohol> <oxygen> attacks <sulfur> of methanesulfonyl <chloride>, <chloride> leaves, and <triethylamine> removes the O–H <proton>. This gives an \b[O-mesylate with retention of the <carbon> configuration]: the original <carbon>–<oxygen> bond has not been displaced.
An accessible chair places the <mesylate> axial. <triethylamine> then removes the anti axial <hydrogen> on the <carbon> between the <ketone> and <mesylate>. Its C–H bond forms the new C=C bond while the C–O bond expels <mesylate>. The result is the \b[conjugated cyclohexenone].
The neighboring <carbon> on the <acetonide> side has its relevant axial position occupied by its <oxygen> substituent, rather than an anti axial <hydrogen>. The elimination toward the <ketone> is therefore favored both by the trans-diaxial geometry and by <conjugation> of the resulting <alkene> with C=O. The <acetonide> remains intact. No inversion of the original <alcohol> <carbon> is required during <mesylation>, and it becomes planar during elimination.
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