Total number of “hyperconjugable” hydrogens in 1-(3-ethyl-4-methylphenyl)-2-methylprop-1-ylium
There is one obvious $\alpha$-position, which is the tertiary carbon atom adjacent to the carbon carrying positive charge. This contributes one hypercongujation structure. It looks like there are no more apparent structures, but the methyl group that is para to the cation can also participate in hyperconjugation

There are three $\ce{H}$-atoms on the methyl group, which give us three more structures. Thus, there are a total of 4 hyperconjugable hydrogens in this structure.
Interesting to note is that the ethyl group at the meta position does not participate in hyperconjugation. Can you find a reason why?