Multiply $3$ by $ \dfrac{x^2}{6} $ to get $ \dfrac{ 3x^2 }{ 6 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Multiply $ \dfrac{3x^2}{6} $ by $ x^2 $ to get $ \dfrac{ 3x^4 }{ 6 } $.

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.

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

Subtract $30x$ from $ \dfrac{3x^4}{6} $ to get $ \dfrac{ \color{purple}{ 3x^4-180x } }{ 6 }$.

Step 1: Write $ 30x $ 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 $\color{blue}{6}$.

$$ \begin{aligned} \frac{3x^4}{6} -30x & \xlongequal{\text{Step 1}} \frac{3x^4}{6} - \frac{30x}{\color{red}{1}} = \frac{ 3x^4 }{ 6 } - \frac{ 30x \cdot \color{blue}{ 6 }}{ 1 \cdot \color{blue}{ 6 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 3x^4 } }{ 6 } - \frac{ \color{purple}{ 180x } }{ 6 }=\frac{ \color{purple}{ 3x^4-180x } }{ 6 } \end{aligned} $$