Subtract $ \dfrac{2}{r} $ from $ \dfrac{r^2-2r}{4r} $ to get $ \dfrac{ \color{purple}{ r^3-2r^2-8r } }{ 4r^2 }$.

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

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