To divide fractions, you multiply the first fraction by the reciprocal of the second fraction.
So, \( \frac{1}{3} \div \frac{6}{7} \) can be rewritten as:
\[ \frac{1}{3} \times \frac{7}{6} \]
Now, multiply the fractions:
\[ \frac{1 \times 7}{3 \times 6} = \frac{7}{18} \]
Therefore, \( \frac{1}{3} \div \frac{6}{7} = \frac{7}{18} \).