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