Multiply $9$ by $ \dfrac{x}{x-2} $ to get $ \dfrac{ 9x }{ x-2 } $.

Step 1: Write $ 9 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

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

Step 1: Factor numerators and denominators.

Step 2: Cancel common factors.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

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