1-Methylcyclohexane-1,2-diol is warmed with dilute $\mathrm{H}{}_2\mathrm{SO}{}_4$. Assume the tertiary carbocation forms first and that hydride migration is the preferred shift. The major carbonyl product is

The tertiary OH leaves to give the cation at C-1. The hydrogen on C-2 shifts to C-1, which leaves the oxygen on C-2 as a protonated carbonyl and keeps the six-membered ring. After deprotonation the product is 2-methylcyclohexan-1-one (the methyl is now on a CH next to C=O).