Numerical answer type, tolerance 0.5.
Answer: 2
The diol is 3,4-dimethylhexane-3,4-diol. Both carbinol carbons carry one methyl and one ethyl group, so the cation may form at either carbon and the two sides are equivalent. Methyl migration gives the ketone CHX3CHX2COC(CHX3)X2CHX2CHX3 and ethyl migration gives CHX3COC(CHX3)(CHX2CHX3)X2. These are two distinct compounds, so the answer is 2.