Multiply $4$ by $ \dfrac{x^6}{2} $ to get $ \dfrac{ 4x^6 }{ 2 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 4 \cdot \frac{x^6}{2} & \xlongequal{\text{Step 1}} \frac{4}{\color{red}{1}} \cdot \frac{x^6}{2} \xlongequal{\text{Step 2}} \frac{ 4 \cdot x^6 }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x^6 }{ 2 } \end{aligned} $$

Multiply $ \dfrac{4x^6}{2} $ by $ x $ to get $ \dfrac{ 4x^7 }{ 2 } $.

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.

$$ \begin{aligned} \frac{4x^6}{2} \cdot x & \xlongequal{\text{Step 1}} \frac{4x^6}{2} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4x^6 \cdot x }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x^7 }{ 2 } \end{aligned} $$

Subtract $6$ from $ \dfrac{4x^7}{2} $ to get $ \dfrac{ \color{purple}{ 4x^7-12 } }{ 2 }$.

Step 1: Write $ 6 $ 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 $\color{blue}{2}$.

$$ \begin{aligned} \frac{4x^7}{2} -6 & \xlongequal{\text{Step 1}} \frac{4x^7}{2} - \frac{6}{\color{red}{1}} = \frac{ 4x^7 }{ 2 } - \frac{ 6 \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 4x^7 } }{ 2 } - \frac{ \color{purple}{ 12 } }{ 2 }=\frac{ \color{purple}{ 4x^7-12 } }{ 2 } \end{aligned} $$