jmc

We know $|(4\sqrt{2}-4i)(\sqrt{3}+3i)|=|4\sqrt{2}-4i||\sqrt{3}+3i|.$ Calculating the magnitudes gives us $\sqrt{32+16}\cdot \sqrt{3+9}=\sqrt{48}\cdot \sqrt{12}=4\sqrt{3}\cdot 2\sqrt{3}=\boxed{24}$