$$\frac{2}{9} \cdot \frac{3}{8} = \frac{2 \cdot 3}{9 \cdot 8} = \frac{6}{72}$$
Сократим дробь на 6:
$$\frac{6:6}{72:6} = \frac{1}{12}$$
Ответ: $$\frac{1}{12}$$