Expression: $\left( 4{y}^{3} \right) \times \left( \frac{ 3 }{ 4 }x{y}^{4} \right) \times \left( -3{x}^{2}{y}^{2} \right)$
Multiplying a positive and a negative equals a negative: $\left( + \right) \times \left( - \right)=\left( - \right)$ $-4{y}^{3} \times \frac{ 3 }{ 4 }x{y}^{4} \times 3{x}^{2}{y}^{2}$
Cancel out the greatest common factor $4$ $-{y}^{3} \times 3x{y}^{4} \times 3{x}^{2}{y}^{2}$
Calculate the product $-9{x}^{3}{y}^{9}$