Multiply $24$ by $ \dfrac{x^2}{12} $ to get $ \dfrac{ 24x^2 }{ 12 } $.

Step 1: Write $ 24 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 24 \cdot \frac{x^2}{12} & \xlongequal{\text{Step 1}} \frac{24}{\color{red}{1}} \cdot \frac{x^2}{12} \xlongequal{\text{Step 2}} \frac{ 24 \cdot x^2 }{ 1 \cdot 12 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 24x^2 }{ 12 } \end{aligned} $$

Multiply $ \dfrac{24x^2}{12} $ by $ x^2 $ to get $ \dfrac{ 24x^4 }{ 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.

$$ \begin{aligned} \frac{24x^2}{12} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{24x^2}{12} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 24x^2 \cdot x^2 }{ 12 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 24x^4 }{ 12 } \end{aligned} $$

Subtract $6x$ from $ \dfrac{24x^4}{12} $ to get $ \dfrac{ \color{purple}{ 24x^4-72x } }{ 12 }$.

Step 1: Write $ 6x $ 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 $\color{blue}{12}$.

$$ \begin{aligned} \frac{24x^4}{12} -6x & \xlongequal{\text{Step 1}} \frac{24x^4}{12} - \frac{6x}{\color{red}{1}} = \frac{ 24x^4 }{ 12 } - \frac{ 6x \cdot \color{blue}{ 12 }}{ 1 \cdot \color{blue}{ 12 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 24x^4 } }{ 12 } - \frac{ \color{purple}{ 72x } }{ 12 }=\frac{ \color{purple}{ 24x^4-72x } }{ 12 } \end{aligned} $$