Multiply $12$ by $ \dfrac{u^2}{3} $ to get $ \dfrac{ 12u^2 }{ 3 } $.

Step 1: Write $ 12 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Multiply $ \dfrac{12u^2}{3} $ by $ u $ to get $ \dfrac{ 12u^3 }{ 3 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Subtract $ \dfrac{12u^3}{3} $ from $ 24u^3 $ to get $ \dfrac{ \color{purple}{ 60u^3 } }{ 3 }$.

Step 1: Write $ 24u^3 $ 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 first fraction by $\color{blue}{ 3 }$.

$$ \begin{aligned} 24u^3- \frac{12u^3}{3} & \xlongequal{\text{Step 1}} \frac{24u^3}{\color{red}{1}} - \frac{12u^3}{3} = \frac{ 24u^3 \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} - \frac{ 12u^3 }{ 3 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 72u^3 } }{ 3 } - \frac{ \color{purple}{ 12u^3 } }{ 3 }=\frac{ \color{purple}{ 60u^3 } }{ 3 } \end{aligned} $$