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

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.

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

Add $ \dfrac{3x}{4} $ and $ \dfrac{2}{3} $ to get $ \dfrac{ \color{purple}{ 9x+8 } }{ 12 }$.

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}{ 3 }$ and the second by $\color{blue}{ 4 }$.

$$ \begin{aligned} \frac{3x}{4} + \frac{2}{3} & = \frac{ 3x \cdot \color{blue}{ 3 }}{ 4 \cdot \color{blue}{ 3 }} + \frac{ 2 \cdot \color{blue}{ 4 }}{ 3 \cdot \color{blue}{ 4 }} = \\[1ex] &=\frac{ \color{purple}{ 9x } }{ 12 } + \frac{ \color{purple}{ 8 } }{ 12 }=\frac{ \color{purple}{ 9x+8 } }{ 12 } \end{aligned} $$