Multiply $ \dfrac{8}{3} $ by $ x^2 $ to get $ \dfrac{ 8x^2 }{ 3 } $.

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.

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

Multiply $ \dfrac{5}{4} $ by $ x $ to get $ \dfrac{ 5x }{ 4 } $.

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.

$$ \begin{aligned} \frac{5}{4} \cdot x & \xlongequal{\text{Step 1}} \frac{5}{4} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5 \cdot x }{ 4 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 5x }{ 4 } \end{aligned} $$

Subtract $ \dfrac{5x}{4} $ from $ \dfrac{8x^2}{3} $ to get $ \dfrac{ \color{purple}{ 32x^2-15x } }{ 12 }$.

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}{ 4 }$ and the second by $\color{blue}{ 3 }$.

$$ \begin{aligned} \frac{8x^2}{3} - \frac{5x}{4} & = \frac{ 8x^2 \cdot \color{blue}{ 4 }}{ 3 \cdot \color{blue}{ 4 }} - \frac{ 5x \cdot \color{blue}{ 3 }}{ 4 \cdot \color{blue}{ 3 }} = \\[1ex] &=\frac{ \color{purple}{ 32x^2 } }{ 12 } - \frac{ \color{purple}{ 15x } }{ 12 }=\frac{ \color{purple}{ 32x^2-15x } }{ 12 } \end{aligned} $$