jmc

Simplify the two factors first. Factor $2^4$ from $576$ to get $36$, and since $36=6^2$, the fourth root of $576$ is $(2^{\frac{4}{4}})(6^{\frac{2}{4}})=2\sqrt{6}$. Because $6^2$ evenly divides $216$, the square root of $216$ is $(6^{\frac{2}{2}})(6^{\frac{1}{2}})=6\sqrt{6}$. Multiply those two quantities together to obtain $\boxed{72}$ as an answer.