The Lewis structure of \(PBr_4^+\) shows that there are a total of 44 valence electrons.

Phosphorus is in group 15, so it has 5 valence electrons.

Bromine is in group 17, so it has 7 valence electrons.

There is one extra electron because of the positive charge.

So the total number of valence electrons is:

$$5 + 4(7) + 1 = 44$$