jmc

Since $q(4)=3\cdot 4-b=12-b$, we can write $p(q(4))=7$ as $p(12-b)=7$. Since $p(x)=2x-7$, we have $p(12-b)=2(12-b)-7=17-2b$. Substituting this into $p(12-b)=7$ gives $17-2b=7$, from which we have $b=\boxed{5}$.