Subtract $ \dfrac{1}{5} $ from $ \dfrac{6}{2x-4} $ to get $ \dfrac{ \color{purple}{ -2x+34 } }{ 10x-20 }$.

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}{ 5 }$ and the second by $\color{blue}{ 2x-4 }$.

$$ \begin{aligned} \frac{6}{2x-4} - \frac{1}{5} & = \frac{ 6 \cdot \color{blue}{ 5 }}{ \left( 2x-4 \right) \cdot \color{blue}{ 5 }} - \frac{ 1 \cdot \color{blue}{ \left( 2x-4 \right) }}{ 5 \cdot \color{blue}{ \left( 2x-4 \right) }} = \\[1ex] &=\frac{ \color{purple}{ 30 } }{ 10x-20 } - \frac{ \color{purple}{ 2x-4 } }{ 10x-20 }=\frac{ \color{purple}{ 30 - \left( 2x-4 \right) } }{ 10x-20 } = \\[1ex] &=\frac{ \color{purple}{ -2x+34 } }{ 10x-20 } \end{aligned} $$