Multiply $8$ by $ \dfrac{x^3}{6} $ to get $ \dfrac{ 8x^3 }{ 6 } $.

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.

$$ \begin{aligned} 8 \cdot \frac{x^3}{6} & \xlongequal{\text{Step 1}} \frac{8}{\color{red}{1}} \cdot \frac{x^3}{6} \xlongequal{\text{Step 2}} \frac{ 8 \cdot x^3 }{ 1 \cdot 6 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 8x^3 }{ 6 } \end{aligned} $$

Multiply $ \dfrac{25}{3} $ by $ x $ to get $ \dfrac{ 25x }{ 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.

$$ \begin{aligned} \frac{25}{3} \cdot x & \xlongequal{\text{Step 1}} \frac{25}{3} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 25 \cdot x }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 25x }{ 3 } \end{aligned} $$

Subtract $10x-4x^2$ from $ \dfrac{-8x^3}{6} $ to get $ \dfrac{ \color{purple}{ -8x^3+24x^2-60x } }{ 6 }$.

Step 1: Write $ 10x-4x^2 $ 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 $\color{blue}{6}$.

$$ \begin{aligned} \frac{-8x^3}{6} -10x-4x^2 & \xlongequal{\text{Step 1}} \frac{-8x^3}{6} - \frac{10x-4x^2}{\color{red}{1}} = \frac{ -8x^3 }{ 6 } - \frac{ \left( 10x-4x^2 \right) \cdot \color{blue}{ 6 }}{ 1 \cdot \color{blue}{ 6 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -8x^3 } }{ 6 } - \frac{ \color{purple}{ 60x-24x^2 } }{ 6 }=\frac{ \color{purple}{ -8x^3 - \left( 60x-24x^2 \right) } }{ 6 } = \\[1ex] &=\frac{ \color{purple}{ -8x^3+24x^2-60x } }{ 6 } \end{aligned} $$

Multiply $ \dfrac{25}{3} $ by $ x $ to get $ \dfrac{ 25x }{ 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.

$$ \begin{aligned} \frac{25}{3} \cdot x & \xlongequal{\text{Step 1}} \frac{25}{3} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 25 \cdot x }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 25x }{ 3 } \end{aligned} $$

Add $ \dfrac{-8x^3+24x^2-60x}{6} $ and $ \dfrac{25x}{3} $ to get $ \dfrac{ \color{purple}{ -8x^3+24x^2-10x } }{ 6 }$.

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

$$ \begin{aligned} \frac{-8x^3+24x^2-60x}{6} + \frac{25x}{3} & = \frac{ -8x^3+24x^2-60x }{ 6 } + \frac{ 25x \cdot \color{blue}{ 2 }}{ 3 \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ -8x^3+24x^2-60x } }{ 6 } + \frac{ \color{purple}{ 50x } }{ 6 }=\frac{ \color{purple}{ -8x^3+24x^2-10x } }{ 6 } \end{aligned} $$