Multiply $ \dfrac{x-2}{2} $ by $ 8x-20 $ to get $ \dfrac{8x^2-36x+40}{2} $.

Step 1: Write $ 8x-20 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{x-2}{2} \cdot 8x-20 & \xlongequal{\text{Step 1}} \frac{x-2}{2} \cdot \frac{8x-20}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( x-2 \right) \cdot \left( 8x-20 \right) }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 8x^2-20x-16x+40 }{ 2 } = \frac{8x^2-36x+40}{2} \end{aligned} $$

Add $ \dfrac{-8x^2+36x-40}{2} $ and $ \dfrac{25}{6} $ to get $ \dfrac{ \color{purple}{ -24x^2+108x-95 } }{ 6 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 3 }$.

$$ \begin{aligned} \frac{-8x^2+36x-40}{2} + \frac{25}{6} & = \frac{ \left( -8x^2+36x-40 \right) \cdot \color{blue}{ 3 }}{ 2 \cdot \color{blue}{ 3 }} + \frac{ 25 }{ 6 } = \\[1ex] &=\frac{ \color{purple}{ -24x^2+108x-120 } }{ 6 } + \frac{ \color{purple}{ 25 } }{ 6 }=\frac{ \color{purple}{ -24x^2+108x-95 } }{ 6 } \end{aligned} $$