Multiply $ \dfrac{x}{3x-18} $ by $ \dfrac{x^2-6x}{2} $ to get $ \dfrac{ x^2 }{ 6 } $.

Step 1: Factor numerators and denominators.

Step 2: Cancel common factors.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{x}{3x-18} \cdot \frac{x^2-6x}{2} & \xlongequal{\text{Step 1}} \frac{ x }{ 3 \cdot \color{red}{ \left( x-6 \right) } } \cdot \frac{ x \cdot \color{red}{ \left( x-6 \right) } }{ 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ x }{ 3 } \cdot \frac{ x }{ 2 } \xlongequal{\text{Step 3}} \frac{ x \cdot x }{ 3 \cdot 2 } \xlongequal{\text{Step 4}} \frac{ x^2 }{ 6 } \end{aligned} $$