To solve the multiplication of the fractions \( \frac{3}{7} \) and \( \frac{2}{5} \), you multiply the numerators together and the denominators together:
\[ \frac{3}{7} \times \frac{2}{5} = \frac{3 \times 2}{7 \times 5} = \frac{6}{35} \]
So, \( \frac{3}{7} \times \frac{2}{5} = \frac{6}{35} \).