The number of $\alpha$ C-H bonds that can take part in hyperconjugation in the 2-methylbutan-2-yl radical $\mathrm{CH}{}_3-\mathrm{C}{}^{\bullet }(\mathrm{CH}{}_3)-\mathrm{CH}{}_2-\mathrm{CH}{}_3$ is

The radical carbon is C2. Its three attached carbons are two methyl groups and one $\mathrm{CH}{}_2$ group of the ethyl chain. The $\alpha$ hydrogens are $3+3+2=8$.