To multiply the fractions \( \frac{15}{4} \) and \( \frac{6}{5} \), you multiply the numerators together and the denominators together.
\[ \frac{15}{4} \times \frac{6}{5} = \frac{15 \times 6}{4 \times 5} \]
Calculating the numerator and denominator:
\[ 15 \times 6 = 90 \] \[ 4 \times 5 = 20 \]
So, we have:
\[ \frac{90}{20} \]
Now, simplify the fraction:
\[ \frac{90 \div 10}{20 \div 10} = \frac{9}{2} \]
Thus, the result is:
\[ \frac{9}{2} \text{ or } 4.5 \]