Multiply $8$ by $ \dfrac{x^3}{14} $ to get $ \dfrac{ 8x^3 }{ 14 } $.

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.

$$ \begin{aligned} 8 \cdot \frac{x^3}{14} & \xlongequal{\text{Step 1}} \frac{8}{\color{red}{1}} \cdot \frac{x^3}{14} \xlongequal{\text{Step 2}} \frac{ 8 \cdot x^3 }{ 1 \cdot 14 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 8x^3 }{ 14 } \end{aligned} $$

Multiply $ \dfrac{8x^3}{14} $ by $ v^2 $ to get $ \dfrac{ 8v^2x^3 }{ 14 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{8x^3}{14} \cdot v^2 & \xlongequal{\text{Step 1}} \frac{8x^3}{14} \cdot \frac{v^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 8x^3 \cdot v^2 }{ 14 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 8v^2x^3 }{ 14 } \end{aligned} $$

Subtract $6x$ from $ \dfrac{8v^2x^3}{14} $ to get $ \dfrac{ \color{purple}{ 8v^2x^3-84x } }{ 14 }$.

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 $\color{blue}{14}$.

$$ \begin{aligned} \frac{8v^2x^3}{14} -6x & \xlongequal{\text{Step 1}} \frac{8v^2x^3}{14} - \frac{6x}{\color{red}{1}} = \frac{ 8v^2x^3 }{ 14 } - \frac{ 6x \cdot \color{blue}{ 14 }}{ 1 \cdot \color{blue}{ 14 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 8v^2x^3 } }{ 14 } - \frac{ \color{purple}{ 84x } }{ 14 }=\frac{ \color{purple}{ 8v^2x^3-84x } }{ 14 } \end{aligned} $$