To multiply the fractions \( \frac{8}{5} \) and \( \frac{3}{10} \), you multiply the numerators together and the denominators together:
\[ \frac{8 \times 3}{5 \times 10} = \frac{24}{50} \]
Now, we can simplify \( \frac{24}{50} \):
Both the numerator and the denominator can be divided by 2:
\[ \frac{24 \div 2}{50 \div 2} = \frac{12}{25} \]
So, \( \frac{8}{5} \times \frac{3}{10} = \frac{12}{25} \).