6. 3 4/7 : (1 1/7 * 2/3) =

6. $$3 \frac{4}{7} : (1 \frac{1}{7} \cdot \frac{2}{3}) = \frac{25}{7} : (\frac{8}{7} \cdot \frac{2}{3}) = \frac{25}{7} : \frac{16}{21} = \frac{25}{7} \cdot \frac{21}{16} = \frac{25 \cdot 3}{1 \cdot 16} = \frac{75}{16} = 4 \frac{11}{16}$$

Ответ: 4 11/16