Multiply $ \dfrac{x-2}{2} $ by $ 4x-10 $ to get $ \dfrac{4x^2-18x+20}{2} $.

Step 1: Write $ 4x-10 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{x-2}{2} \cdot 4x-10 & \xlongequal{\text{Step 1}} \frac{x-2}{2} \cdot \frac{4x-10}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( x-2 \right) \cdot \left( 4x-10 \right) }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x^2-10x-8x+20 }{ 2 } = \frac{4x^2-18x+20}{2} \end{aligned} $$

Subtract $ \dfrac{25}{6} $ from $ \dfrac{4x^2-18x+20}{2} $ to get $ \dfrac{ \color{purple}{ 12x^2-54x+35 } }{ 6 }$.

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

$$ \begin{aligned} \frac{4x^2-18x+20}{2} - \frac{25}{6} & = \frac{ \left( 4x^2-18x+20 \right) \cdot \color{blue}{ 3 }}{ 2 \cdot \color{blue}{ 3 }} - \frac{ 25 }{ 6 } = \\[1ex] &=\frac{ \color{purple}{ 12x^2-54x+60 } }{ 6 } - \frac{ \color{purple}{ 25 } }{ 6 }=\frac{ \color{purple}{ 12x^2-54x+35 } }{ 6 } \end{aligned} $$