Divide both the top and bottom numbers by $ \color{orangered}{ 4 } $.

Add $ \dfrac{9}{2} $ and $ \dfrac{2}{3} $ to get $ \dfrac{ \color{purple}{ 31 } }{ 6 }$.

To add fractions they must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ 3 }$ and the second by $\color{blue}{ 2 }$.

$$ \begin{aligned} \frac{9}{2} + \frac{2}{3} & = \frac{ 9 \cdot \color{blue}{ 3 }}{ 2 \cdot \color{blue}{ 3 }} + \frac{ 2 \cdot \color{blue}{ 2 }}{ 3 \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ 27 } }{ 6 } + \frac{ \color{purple}{ 4 } }{ 6 }=\frac{ \color{purple}{ 31 } }{ 6 } \end{aligned} $$