 Solution

This is an acid-catalysed alpha-ketol rearrangement. Label the original ketone carbon $C_A$ and the adjacent tertiary alcohol carbon $C_B$. Protonate the oxygen on $C_A$ to activate that carbonyl. The appropriately aligned cage C–C sigma bond attached to $C_B$ migrates onto $C_A$, while the hydroxyl oxygen at $C_B$ supplies its lone pair to form the new $C_B=O$ bond. At the same time the old $C_A=O$ pi bond moves onto oxygen, which becomes the new $C_A$–OH. deprotonation regenerates the acid.

The migration reroutes the bridge rather than removing water: the original alcohol carbon becomes the ketone, and the original ketone carbon becomes the tertiary alcohol. A productive conformation aligns the migrating sigma orbital with the accepting carbonyl pi-star orbital; the oxygen lone pair simultaneously overlaps the developing p orbital at the donor carbon. The cage's geometry controls which adjacent sigma bond has the necessary alignment and which less strained skeletal isomer results. A freely rotating isolated carbocation or a simple proton shift cannot account for the changed cage connectivity.