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