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

Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{r}$.

$$ \begin{aligned} \frac{2r-4}{r} -2 & \xlongequal{\text{Step 1}} \frac{2r-4}{r} - \frac{2}{\color{red}{1}} = \frac{ 2r-4 }{ r } - \frac{ 2 \cdot \color{blue}{ r }}{ 1 \cdot \color{blue}{ r }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2r-4 } }{ r } - \frac{ \color{purple}{ 2r } }{ r }=\frac{ \color{purple}{ -4 } }{ r } \end{aligned} $$