The number of alpha hydrogens (hydrogens on carbons attached directly to the cationic carbon) in the 3-ethylpentan-3-yl cation, $(\mathrm{CH}{}_3\mathrm{CH}{}_2){}_3\mathrm{C}{}^{+}$, is:

The cationic carbon bears three ethyl groups, and each has one alpha carbon ($\mathrm{CH}{}_2$) with 2 hydrogens. Total $=3\times 2=6$. The 9 hydrogens of the methyl groups are beta and do not take part in hyperconjugation.