$$\begin{aligned} &-3\frac{1}{7}\cdot(-8)-2,9:0,1+\frac{11}{21}:\left(-\frac{2}{3}\right)=\\ &=-\frac{22}{7}\cdot(-8)-\frac{29}{10}:\frac{1}{10}+\frac{11}{21}:\left(-\frac{2}{3}\right)=\\ &=\frac{176}{7}-\frac{29}{10}\cdot10+\frac{11}{21}\cdot\left(-\frac{3}{2}\right)=\\ &=\frac{176}{7}-29+\frac{11}{7}\cdot\left(-\frac{1}{2}\right)=\\ &=\frac{176}{7}-29-\frac{11}{14}=\\ &=\frac{352}{14}-\frac{29\cdot14}{14}-\frac{11}{14}=\\ &=\frac{352-406-11}{14}=\\ &=\frac{-65}{14}=\\ &=-4\frac{9}{14} \end{aligned}$$
Ответ: $$-4\frac{9}{14}$$