smc

This problem can be converted to a system of equations. Let $p$ be Pete's current age and $c$ be Claire's current age. The first statement can be written as $p-2=3(c-2)$. The second statement can be written as $p-4=4(c-4)$ To solve the system of equations: $p=3c-4$ $p=4c-12$ $3c-4=4c-12$ $c=8$ $p=20.$ Let $x$ be the number of years until Pete is twice as old as his cousin. $20+x=2(8+x)$ $20+x=16+2x$ $x=4$ The answer is $\boxed{4}$.