4) \( -\frac{6}{5} x^{3} y^{2} \cdot \frac{15}{4} x^{6} y^{5} \)

To simplify the expression \( -\frac{6}{5} x^{3} y^{2} \cdot \frac{15}{4} x^{6} y^{5} \), start by multiplying the coefficients. Multiply \(-\frac{6}{5}\) by \(\frac{15}{4}\), which results in \(-\frac{90}{20} = -\frac{9}{2}\). Next, combine the variable parts by adding the exponents of like bases: \(x^{3} \cdot x^{6} = x^{3+6} = x^{9}\) and \(y^{2} \cdot y^{5} = y^{2+5} = y^{7}\). Putting it all together, you get the simplified expression: \(-\frac{9}{2} x^{9} y^{7}\).