Multiply $ \dfrac{3x-12}{x+5} $ by $ \dfrac{x+6}{2x-8} $ to get $ \dfrac{ 3x+18 }{ 2x+10 } $.

Step 1: Factor numerators and denominators.

Step 2: Cancel common factors.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{3x-12}{x+5} \cdot \frac{x+6}{2x-8} & \xlongequal{\text{Step 1}} \frac{ 3 \cdot \color{blue}{ \left( x-4 \right) } }{ x+5 } \cdot \frac{ x+6 }{ 2 \cdot \color{blue}{ \left( x-4 \right) } } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 3 }{ x+5 } \cdot \frac{ x+6 }{ 2 } \xlongequal{\text{Step 3}} \frac{ 3 \cdot \left( x+6 \right) }{ \left( x+5 \right) \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ 3x+18 }{ 2x+10 } \end{aligned} $$