6. Given in $\triangle A B C$, $\angle B A C=\frac{2 \pi}{3}, A B=2, A C=1, D$ is a point on side $B C$, $D C=2 B D$, then $\overrightarrow{A D} \cdot \overrightarrow{B C}=$ $\qquad$
Answer: $-\frac{8}{3}$