The alcohol shown is heated with concentrated $\mathrm{H}{}_2\mathrm{SO}{}_4$. Count every different alkene (constitutional isomers; none of them shows geometrical isomerism) that can be formed either by direct loss of water or after a single 1,2-methyl shift of the first cation. Answer as an integer.

The alcohol is 3,3-dimethylbutan-2-ol. Direct elimination can use only the methyl hydrogens (the other neighbour is quaternary) and gives 3,3-dimethylbut-1-ene. A methyl shift turns the secondary cation into the tertiary 2,3-dimethylbutan-2-yl cation, which loses $\mathrm{H}{}^{+}$ to give 2,3-dimethylbut-2-ene or 2,3-dimethylbut-1-ene. That makes 3 alkenes.