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

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

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

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.

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

Subtract $4x$ from $ \dfrac{2x^4}{3} $ to get $ \dfrac{ \color{purple}{ 2x^4-12x } }{ 3 }$.

Step 1: Write $ 4x $ 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 $\color{blue}{3}$.

$$ \begin{aligned} \frac{2x^4}{3} -4x & \xlongequal{\text{Step 1}} \frac{2x^4}{3} - \frac{4x}{\color{red}{1}} = \frac{ 2x^4 }{ 3 } - \frac{ 4x \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2x^4 } }{ 3 } - \frac{ \color{purple}{ 12x } }{ 3 }=\frac{ \color{purple}{ 2x^4-12x } }{ 3 } \end{aligned} $$