Solve for $p$: $3p - 2(p-4) = 7p + 6$
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 $p = 2/6 = \boxed{\frac{1}{3}}$.