How do you convert the polar coordinate (4, 315) into cartesian coordinates?

Answer is $\left(4 \cos 315 , 4 \sin 315\right)$
In polar coordinate if you have $\left(r , \theta\right)$ then the corresponding cartesian coordinate will be $\left(r \cos \theta , r \sin \theta\right) .$
So your answer is $\left(4 \cos 315 , 4 \sin 315\right)$.