jmc

Point $G$ is the centroid of $△DEF$, so $DG:GP=EG:GQ=2:1$. Therefore, $DG=\frac{2}{3}(DP)=12$ and $EG=\frac{2}{3}(EQ)=16$, so applying the Pythagorean Theorem to $△EGD$ gives us $DE=\sqrt{E{G}^2+G{D}^2}=\boxed{20}$.