To multiply the fractions \( \frac{3}{7} \) and \( \frac{4}{9} \), you multiply the numerators together and the denominators together:
\[ \frac{3}{7} \times \frac{4}{9} = \frac{3 \times 4}{7 \times 9} = \frac{12}{63} \]
Now, you can simplify \( \frac{12}{63} \) by finding the greatest common divisor (GCD) of 12 and 63, which is 3:
\[ \frac{12 \div 3}{63 \div 3} = \frac{4}{21} \]
So,
\[ \frac{3}{7} \times \frac{4}{9} = \frac{4}{21} \]