Multiply $6$ by $ \dfrac{x^3}{12} $ to get $ \dfrac{ 6x^3 }{ 12 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 6 \cdot \frac{x^3}{12} & \xlongequal{\text{Step 1}} \frac{6}{\color{red}{1}} \cdot \frac{x^3}{12} \xlongequal{\text{Step 2}} \frac{ 6 \cdot x^3 }{ 1 \cdot 12 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 6x^3 }{ 12 } \end{aligned} $$

Multiply $ \dfrac{6x^3}{12} $ by $ x^2 $ to get $ \dfrac{ 6x^5 }{ 12 } $.

Step 1: Write $ x^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{6x^3}{12} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{6x^3}{12} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 6x^3 \cdot x^2 }{ 12 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 6x^5 }{ 12 } \end{aligned} $$

Subtract $72x$ from $ \dfrac{6x^5}{12} $ to get $ \dfrac{ \color{purple}{ 6x^5-864x } }{ 12 }$.

Step 1: Write $ 72x $ 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 second fraction by $\color{blue}{12}$.

$$ \begin{aligned} \frac{6x^5}{12} -72x & \xlongequal{\text{Step 1}} \frac{6x^5}{12} - \frac{72x}{\color{red}{1}} = \frac{ 6x^5 }{ 12 } - \frac{ 72x \cdot \color{blue}{ 12 }}{ 1 \cdot \color{blue}{ 12 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 6x^5 } }{ 12 } - \frac{ \color{purple}{ 864x } }{ 12 }=\frac{ \color{purple}{ 6x^5-864x } }{ 12 } \end{aligned} $$