Multiply $ \dfrac{4x^2}{x^2-16} $ by $ \dfrac{x^3-64}{2x} $ to get $ \dfrac{ 4x^4+16x^3+64x^2 }{ 2x^2+8x } $.

Step 1: Factor numerators and denominators.

Step 2: Cancel common factors.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{4x^2}{x^2-16} \cdot \frac{x^3-64}{2x} & \xlongequal{\text{Step 1}} \frac{ 4x^2 }{ \left( x+4 \right) \cdot \color{red}{ \left( x-4 \right) } } \cdot \frac{ \left( x^2+4x+16 \right) \cdot \color{red}{ \left( x-4 \right) } }{ 2x } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 4x^2 }{ x+4 } \cdot \frac{ x^2+4x+16 }{ 2x } \xlongequal{\text{Step 3}} \frac{ 4x^2 \cdot \left( x^2+4x+16 \right) }{ \left( x+4 \right) \cdot 2x } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ 4x^4+16x^3+64x^2 }{ 2x^2+8x } \end{aligned} $$