To simplify expressions such as $\sqrt{6}(1 + 3\sqrt{6})$ and $\sqrt[3]{4}(-2 - \sqrt[3]{6})$, apply the Distributive Property and then simplify the resulting terms. For the first expression, distributing gives $\sqrt{6} + 3\sqrt{36}$. Since $\sqrt{36}$ is a perfect square ($6$), the expression simplifies to $\sqrt{6} + 3(6)$, or $\sqrt{6} + 18$. For the second expression, distributing produces $-2\sqrt[3]{4} - \sqrt[3]{24}$. Simplifying the second radical by extracting the perfect cube factor gives $-2\sqrt[3]{4} - \sqrt[3]{8 \cdot 3}$, which becomes $-2\sqrt[3]{4} - 2\sqrt[3]{3}$.