10. 2 6/7 : 5/6 * 9/14 =

10. $$2 \frac{6}{7} : \frac{5}{6} \cdot \frac{9}{14} = \frac{20}{7} : \frac{5}{6} \cdot \frac{9}{14} = \frac{20}{7} : \frac{5 \cdot 9}{6 \cdot 14} = \frac{20}{7} : \frac{45}{84} = \frac{20}{7} \cdot \frac{84}{45} = \frac{20 \cdot 84}{7 \cdot 45} = \frac{4 \cdot 12}{1 \cdot 9} = \frac{48}{9} = 5 \frac{3}{9} = 5 \frac{1}{3}$$

Ответ: 5 1/3