jmc

First, we simplify the left side. We have $$3p-2(p-4)=3p-2p+8=p+8,$$ so we can write the original equation as $p+8=7p+6$. Subtracting $p$ from both sides gives $8=6p+6$, and subtracting 6 from both sides gives $2=6p$. Finally, dividing by 6 gives $p=2/6=\boxed{\frac{1}{3}}$.