Multiply $6$ by $ \dfrac{x^3}{7} $ to get $ \dfrac{ 6x^3 }{ 7 } $.

Step 1: Write $ 6 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Multiply $ \dfrac{6x^3}{7} $ by $ x^3 $ to get $ \dfrac{ 6x^6 }{ 7 } $.

Step 1: Write $ x^3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Add $x^4$ and $ \dfrac{6x^6}{7} $ to get $ \dfrac{ \color{purple}{ 6x^6+7x^4 } }{ 7 }$.

Step 1: Write $ x^4 $ 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 $\color{blue}{ 7 }$.

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