To multiply the fractions \( \frac{24}{5} \) and \( \frac{8}{19} \), you multiply the numerators together and the denominators together:
\[ \frac{24 \times 8}{5 \times 19} \]
Calculating the numerator:
\[ 24 \times 8 = 192 \]
Calculating the denominator:
\[ 5 \times 19 = 95 \]
Putting it all together, we have:
\[ \frac{192}{95} \]
This fraction is in its simplest form since 192 and 95 have no common factors other than 1. So the final answer is:
\[ \frac{192}{95} \]