Multiply $ \dfrac{5}{3} $ by $ w $ to get $ \dfrac{ 5w }{ 3 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{5}{3} \cdot w & \xlongequal{\text{Step 1}} \frac{5}{3} \cdot \frac{w}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5 \cdot w }{ 3 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 5w }{ 3 } \end{aligned} $$

Multiply $ \dfrac{5w}{3} $ by $ x $ to get $ \dfrac{ 5wx }{ 3 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{5w}{3} \cdot x & \xlongequal{\text{Step 1}} \frac{5w}{3} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5w \cdot x }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5wx }{ 3 } \end{aligned} $$

Subtract $ \dfrac{5wx}{3} $ from $ 6x-6 $ to get $ \dfrac{ \color{purple}{ -5wx+18x-18 } }{ 3 }$.

Step 1: Write $ 6x-6 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 3 }$.

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