1-(4-Methoxyphenyl)-2-methyl-1-phenylpropane-1,2-diol, $(4\text{-}\mathrm{CH}{}_3\mathrm{O}-\mathrm{C}{}_6\mathrm{H}{}_4)(\mathrm{C}{}_6\mathrm{H}{}_5)\mathrm{C}(\mathrm{OH})-\mathrm{C}(\mathrm{OH})(\mathrm{CH}{}_3){}_2$, is treated with dilute $\mathrm{H}{}_2\mathrm{SO}{}_4$. The main product is

Loss of the hydroxyl on C-1 gives a diarylcarbenium ion that is far more stable than the tertiary alkyl cation at C-2, and the 4-methoxy group stabilises it further. The only groups on C-2 that can migrate are the two methyls, so one methyl moves to C-1. C-2 becomes $\mathrm{C}(=\mathrm{O})\mathrm{CH}{}_3$ and C-1 becomes $\mathrm{C}(\mathrm{CH}{}_3)(\mathrm{Ar})(\mathrm{Ph})$, giving 3-(4-methoxyphenyl)-3-phenylbutan-2-one.