Multiply $ \color{blue}{3} $ by $ \left( u+2\right) $ $$ \color{blue}{3} \cdot \left( u+2\right) = 3u+6 $$

Subtract $ \dfrac{2}{3u+6} $ from $ \dfrac{1}{4} $ to get $ \dfrac{ \color{purple}{ 3u-2 } }{ 12u+24 }$.

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}{ 3u+6 }$ and the second by $\color{blue}{ 4 }$.

$$ \begin{aligned} \frac{1}{4} - \frac{2}{3u+6} & = \frac{ 1 \cdot \color{blue}{ \left( 3u+6 \right) }}{ 4 \cdot \color{blue}{ \left( 3u+6 \right) }} - \frac{ 2 \cdot \color{blue}{ 4 }}{ \left( 3u+6 \right) \cdot \color{blue}{ 4 }} = \\[1ex] &=\frac{ \color{purple}{ 3u+6 } }{ 12u+24 } - \frac{ \color{purple}{ 8 } }{ 12u+24 }=\frac{ \color{purple}{ 3u-2 } }{ 12u+24 } \end{aligned} $$