Multiply $ \dfrac{2x-4}{3x} $ by $ \dfrac{9x^2}{x-2} $ to get $ \dfrac{ 18x^2 }{ 3x } $.

Step 1: Factor numerators and denominators.

Step 2: Cancel common factors.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{2x-4}{3x} \cdot \frac{9x^2}{x-2} & \xlongequal{\text{Step 1}} \frac{ 2 \cdot \color{blue}{ \left( x-2 \right) } }{ 3x } \cdot \frac{ 9x^2 }{ 1 \cdot \color{blue}{ \left( x-2 \right) } } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 2 }{ 3x } \cdot \frac{ 9x^2 }{ 1 } \xlongequal{\text{Step 3}} \frac{ 2 \cdot 9x^2 }{ 3x \cdot 1 } \xlongequal{\text{Step 4}} \frac{ 18x^2 }{ 3x } \end{aligned} $$