Multiply $ \dfrac{16}{3} $ by $ x $ to get $ \dfrac{ 16x }{ 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.

$$ \begin{aligned} \frac{16}{3} \cdot x & \xlongequal{\text{Step 1}} \frac{16}{3} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 16 \cdot x }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 16x }{ 3 } \end{aligned} $$

Add $x^2-8x$ and $ \dfrac{16x}{3} $ to get $ \dfrac{ \color{purple}{ 3x^2-8x } }{ 3 }$.

Step 1: Write $ x^2-8x $ 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 $\color{blue}{ 3 }$.

$$ \begin{aligned} x^2-8x+ \frac{16x}{3} & \xlongequal{\text{Step 1}} \frac{x^2-8x}{\color{red}{1}} + \frac{16x}{3} = \frac{ \left( x^2-8x \right) \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} + \frac{ 16x }{ 3 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 3x^2-24x } }{ 3 } + \frac{ \color{purple}{ 16x } }{ 3 }=\frac{ \color{purple}{ 3x^2-8x } }{ 3 } \end{aligned} $$

Subtract $12$ from $ \dfrac{3x^2-8x}{3} $ to get $ \dfrac{ \color{purple}{ 3x^2-8x-36 } }{ 3 }$.

Step 1: Write $ 12 $ 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 $\color{blue}{3}$.

$$ \begin{aligned} \frac{3x^2-8x}{3} -12 & \xlongequal{\text{Step 1}} \frac{3x^2-8x}{3} - \frac{12}{\color{red}{1}} = \frac{ 3x^2-8x }{ 3 } - \frac{ 12 \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 3x^2-8x } }{ 3 } - \frac{ \color{purple}{ 36 } }{ 3 }=\frac{ \color{purple}{ 3x^2-8x-36 } }{ 3 } \end{aligned} $$