To multiply the fractions \( \frac{5}{7} \) and \( \frac{6}{9} \), you can multiply the numerators together and the denominators together:
\[ \frac{5}{7} \times \frac{6}{9} = \frac{5 \times 6}{7 \times 9} = \frac{30}{63} \]
Next, you can simplify the fraction \( \frac{30}{63} \). Both the numerator and the denominator can be divided by their greatest common divisor, which is 3:
\[ \frac{30 \div 3}{63 \div 3} = \frac{10}{21} \]
So, the result of \( \frac{5}{7} \times \frac{6}{9} \) is \( \frac{10}{21} \).