Add $-2$ and $ \dfrac{-4}{9} $ to get $ \dfrac{ \color{purple}{ -22 } }{ 9 }$.

Step 1: Write $ -2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add fractions they must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 9 }$.

$$ \begin{aligned} -2+ \frac{-4}{9} & \xlongequal{\text{Step 1}} \frac{-2}{\color{red}{1}} + \frac{-4}{9} = \frac{ \left( -2 \right) \cdot \color{blue}{ 9 }}{ 1 \cdot \color{blue}{ 9 }} + \frac{ -4 }{ 9 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -18 } }{ 9 } + \frac{ \color{purple}{ -4 } }{ 9 }=\frac{ \color{purple}{ -22 } }{ 9 } \end{aligned} $$