To multiply the fractions \( \frac{1}{6} \) and \( \frac{1}{7} \), you multiply the numerators together and the denominators together:
\[ \frac{1}{6} \times \frac{1}{7} = \frac{1 \times 1}{6 \times 7} = \frac{1}{42} \]
So, \( \frac{1}{6} \times \frac{1}{7} = \frac{1}{42} \).