Multiply $8$ by $ \dfrac{x}{12} $ to get $ \dfrac{ 8x }{ 12 } $.

Step 1: Write $ 8 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 8 \cdot \frac{x}{12} & \xlongequal{\text{Step 1}} \frac{8}{\color{red}{1}} \cdot \frac{x}{12} \xlongequal{\text{Step 2}} \frac{ 8 \cdot x }{ 1 \cdot 12 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 8x }{ 12 } \end{aligned} $$

Multiply $ \dfrac{8x}{12} $ by $ x $ to get $ \dfrac{ 8x^2 }{ 12 } $.

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.

$$ \begin{aligned} \frac{8x}{12} \cdot x & \xlongequal{\text{Step 1}} \frac{8x}{12} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 8x \cdot x }{ 12 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 8x^2 }{ 12 } \end{aligned} $$

Add $4x^2$ and $ \dfrac{8x^2}{12} $ to get $ \dfrac{ \color{purple}{ 56x^2 } }{ 12 }$.

Step 1: Write $ 4x^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 12 }$.

$$ \begin{aligned} 4x^2+ \frac{8x^2}{12} & \xlongequal{\text{Step 1}} \frac{4x^2}{\color{red}{1}} + \frac{8x^2}{12} = \frac{ 4x^2 \cdot \color{blue}{ 12 }}{ 1 \cdot \color{blue}{ 12 }} + \frac{ 8x^2 }{ 12 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 48x^2 } }{ 12 } + \frac{ \color{purple}{ 8x^2 } }{ 12 }=\frac{ \color{purple}{ 56x^2 } }{ 12 } \end{aligned} $$

Add $ \dfrac{56x^2}{12} $ and $ 24 $ to get $ \dfrac{ \color{purple}{ 56x^2+288 } }{ 12 }$.

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

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{12}$.

$$ \begin{aligned} \frac{56x^2}{12} +24 & \xlongequal{\text{Step 1}} \frac{56x^2}{12} + \frac{24}{\color{red}{1}} = \frac{ 56x^2 }{ 12 } + \frac{ 24 \cdot \color{blue}{ 12 }}{ 1 \cdot \color{blue}{ 12 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 56x^2 } }{ 12 } + \frac{ \color{purple}{ 288 } }{ 12 }=\frac{ \color{purple}{ 56x^2+288 } }{ 12 } \end{aligned} $$