Multiply $4$ by $ \dfrac{x}{12} $ to get $ \dfrac{ 4x }{ 12 } $.

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.

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

Multiply $12$ by $ \dfrac{x}{x+3} $ to get $ \dfrac{ 12x }{ x+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.

$$ \begin{aligned} 12 \cdot \frac{x}{x+3} & \xlongequal{\text{Step 1}} \frac{12}{\color{red}{1}} \cdot \frac{x}{x+3} \xlongequal{\text{Step 2}} \frac{ 12 \cdot x }{ 1 \cdot \left( x+3 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 12x }{ x+3 } \end{aligned} $$

Add $ \dfrac{4x}{12} $ and $ \dfrac{12x}{x+3} $ to get $ \dfrac{ \color{purple}{ 4x^2+156x } }{ 12x+36 }$.

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}{ x+3 }$ and the second by $\color{blue}{ 12 }$.

$$ \begin{aligned} \frac{4x}{12} + \frac{12x}{x+3} & = \frac{ 4x \cdot \color{blue}{ \left( x+3 \right) }}{ 12 \cdot \color{blue}{ \left( x+3 \right) }} + \frac{ 12x \cdot \color{blue}{ 12 }}{ \left( x+3 \right) \cdot \color{blue}{ 12 }} = \\[1ex] &=\frac{ \color{purple}{ 4x^2+12x } }{ 12x+36 } + \frac{ \color{purple}{ 144x } }{ 12x+36 }=\frac{ \color{purple}{ 4x^2+156x } }{ 12x+36 } \end{aligned} $$