To multiply the fractions \( \frac{3}{4} \) and \( \frac{4}{5} \), you multiply the numerators together and the denominators together:
\[ \frac{3}{4} \times \frac{4}{5} = \frac{3 \times 4}{4 \times 5} = \frac{12}{20} \]
Next, we can simplify \( \frac{12}{20} \) by finding the greatest common divisor (GCD) of 12 and 20, which is 4:
\[ \frac{12 \div 4}{20 \div 4} = \frac{3}{5} \]
Thus, \( \frac{3}{4} \times \frac{4}{5} = \frac{3}{5} \).