$$\frac{8}{9} : \frac{2}{3} = \frac{8}{9} \cdot \frac{3}{2} = \frac{8 \cdot 3}{9 \cdot 2} = \frac{24}{18} = \frac{4}{3} = 1\frac{1}{3}$$
Ответ: 1 1/3