jmc

First, we label the diagram:



Triangle $ABD$ is a 30-60-90 triangle, so $AB=BD/2=4$ and $AD=AB\sqrt{3}=4\sqrt{3}$.

Triangle $ACD$ is a 45-45-90 triangle, so $CD=AC\sqrt{2}=4\sqrt{3}\cdot \sqrt{2}=\boxed{4\sqrt{6}}$.