Add $ \dfrac{1}{2} $ and $ \dfrac{1}{2+h} $ to get $ \dfrac{ \color{purple}{ h+4 } }{ 2h+4 }$.

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}{ h+2 }$ and the second by $\color{blue}{ 2 }$.

$$ \begin{aligned} \frac{1}{2} + \frac{1}{2+h} & = \frac{ 1 \cdot \color{blue}{ \left( h+2 \right) }}{ 2 \cdot \color{blue}{ \left( h+2 \right) }} + \frac{ 1 \cdot \color{blue}{ 2 }}{ \left( 2+h \right) \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ h+2 } }{ 2h+4 } + \frac{ \color{purple}{ 2 } }{ 2h+4 }=\frac{ \color{purple}{ h+4 } }{ 2h+4 } \end{aligned} $$