54. As shown in the figure, in quadrilateral $A B C D$, $\angle B=135^{\circ}, \angle C=120^{\circ}, A B=2 \sqrt{3}, B C=4-2 \sqrt{2}$, $C D=4 \sqrt{2}$, then the length of side $A D$ is ( ).
(A) $2 \sqrt{6}$
(B) $4 \sqrt{6}$
(C) $4+\sqrt{6}$
(D) $2+2 \sqrt{6}$
Answer: D