Question: A regular hexagon of side length 4 is embedded in a regular octagon of side length 4, as shown. What is the area of quadrilateral $A B C D$ ? A) $16 \sqrt{2}$  B)  $16 \sqrt{3}$  C) $16+16 \sqrt{2}-16 \sqrt{3}$   D) $16+16 \sqrt{3}-16 \sqrt{2}$. Please choose an answer from [A, B, C, D].
Answer: C