To calculate the product of \(\frac{2}{5}\) and \(\frac{3}{4}\), you multiply the numerators together and the denominators together:
\[ \frac{2}{5} \times \frac{3}{4} = \frac{2 \times 3}{5 \times 4} = \frac{6}{20} \]
Now, simplify \(\frac{6}{20}\) by finding the greatest common divisor of 6 and 20, which is 2:
\[ \frac{6 \div 2}{20 \div 2} = \frac{3}{10} \]
Thus, the product of \(\frac{2}{5}\) and \(\frac{3}{4}\) is \(\frac{3}{10}\).