jmc

First, we simplify $\sqrt{24}$ by noting that $24=4\cdot 6$, so $\sqrt{24}=\sqrt{4}\cdot \sqrt{6}=2\sqrt{6}$. Therefore, we have $\sqrt{6}+\sqrt{24}=\sqrt{6}+2\sqrt{6}=3\sqrt{6}$, so $$(\sqrt{6}+\sqrt{24}{)}^2=(3\sqrt{6}{)}^2=3^2\cdot (\sqrt{6}{)}^2=9\cdot 6=\boxed{54}.$$