Add $ \dfrac{x-4}{2x} $ and $ \dfrac{4x}{3} $ to get $ \dfrac{ \color{purple}{ 8x^2+3x-12 } }{ 6x }$.

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 $\color{blue}{ 2x }$.

$$ \begin{aligned} \frac{x-4}{2x} + \frac{4x}{3} & = \frac{ \left( x-4 \right) \cdot \color{blue}{ 3 }}{ 2x \cdot \color{blue}{ 3 }} + \frac{ 4x \cdot \color{blue}{ 2x }}{ 3 \cdot \color{blue}{ 2x }} = \\[1ex] &=\frac{ \color{purple}{ 3x-12 } }{ 6x } + \frac{ \color{purple}{ 8x^2 } }{ 6x }=\frac{ \color{purple}{ 8x^2+3x-12 } }{ 6x } \end{aligned} $$

Add $ \dfrac{8x^2+3x-12}{6x} $ and $ \dfrac{x+2}{x} $ to get $ \dfrac{ \color{purple}{ 8x^3+9x^2 } }{ 6x^2 }$.

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 }$ and the second by $\color{blue}{ 6x }$.

$$ \begin{aligned} \frac{8x^2+3x-12}{6x} + \frac{x+2}{x} & = \frac{ \left( 8x^2+3x-12 \right) \cdot \color{blue}{ x }}{ 6x \cdot \color{blue}{ x }} + \frac{ \left( x+2 \right) \cdot \color{blue}{ 6x }}{ x \cdot \color{blue}{ 6x }} = \\[1ex] &=\frac{ \color{purple}{ 8x^3+3x^2-12x } }{ 6x^2 } + \frac{ \color{purple}{ 6x^2+12x } }{ 6x^2 }=\frac{ \color{purple}{ 8x^3+9x^2 } }{ 6x^2 } \end{aligned} $$