6. Найдите значение выражения: $$2-\frac{4}{15}\cdot(2-\frac{1}{15}):\frac{4}{2+\frac{2}{3}}$$

$$2-\frac{4}{15}\cdot(2-\frac{1}{15}):\frac{4}{2+\frac{2}{3}}=2-\frac{4}{15}\cdot(\frac{30}{15}-\frac{1}{15}):\frac{4}{\frac{6}{3}+\frac{2}{3}}=2-\frac{4}{15}\cdot\frac{29}{15}:\frac{4}{\frac{8}{3}}=2-\frac{4}{15}\cdot\frac{29}{15}\cdot\frac{8}{4}=2-\frac{4\cdot29\cdot8}{15\cdot15\cdot4}=2-\frac{29\cdot8}{15\cdot15}=2-\frac{232}{225}=\frac{450}{225}-\frac{232}{225}=\frac{218}{225}$$

Ответ: $$\frac{218}{225}$$