The number of alpha hydrogens (hence of hyperconjugative structures) in the tert-butyl cation $(\mathrm{CH}{}_3){}_3\mathrm{C}{}^{+}$ is

Each of the three methyl groups attached to the cationic carbon carries 3 alpha C-H bonds, so $3\times 3=9$. The hyperconjugative structures number 9.