Add $ \dfrac{k}{4} $ and $ \dfrac{k-6}{4k-4} $ to get $ \dfrac{ \color{purple}{ 4k^2-24 } }{ 16k-16 }$.

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

$$ \begin{aligned} \frac{k}{4} + \frac{k-6}{4k-4} & = \frac{ k \cdot \color{blue}{ \left( 4k-4 \right) }}{ 4 \cdot \color{blue}{ \left( 4k-4 \right) }} + \frac{ \left( k-6 \right) \cdot \color{blue}{ 4 }}{ \left( 4k-4 \right) \cdot \color{blue}{ 4 }} = \\[1ex] &=\frac{ \color{purple}{ 4k^2-4k } }{ 16k-16 } + \frac{ \color{purple}{ 4k-24 } }{ 16k-16 }=\frac{ \color{purple}{ 4k^2-24 } }{ 16k-16 } \end{aligned} $$