$$\frac{1}{6} \cdot \frac{2}{7} = \frac{1 \cdot 2}{6 \cdot 7} = \frac{2}{42}$$
Сократим дробь на 2:
$$\frac{2:2}{42:2} = \frac{1}{21}$$
Ответ: $$\frac{1}{21}$$