To divide the fractions \( \frac{6}{7} \) by \( \frac{3}{5} \), you can multiply by the reciprocal of the second fraction.
Thus, the calculation looks like this:
\[ \frac{6}{7} \div \frac{3}{5} = \frac{6}{7} \times \frac{5}{3} \]
Now, multiply the numerators and the denominators:
\[ \frac{6 \times 5}{7 \times 3} = \frac{30}{21} \]
Now we can simplify \( \frac{30}{21} \). Both 30 and 21 can be divided by 3:
\[ \frac{30 \div 3}{21 \div 3} = \frac{10}{7} \]
Thus, the result of \( \frac{6}{7} \div \frac{3}{5} \) is:
\[ \frac{10}{7} \]