jmc

Since opposite sides of a parallelogram have the same length, we have the equations $$AB=CD\Rightarrow 38=2x+4\Rightarrow x=17$$and $$BC=AD\Rightarrow 3y^3=24\Rightarrow y=2.$$The product of $x$ and $y$ is then $17\cdot 2=\boxed{34}$.