Add $ \dfrac{6+10i}{3} $ and $ \dfrac{4i}{3} $ to get $ \dfrac{14i+6}{3} $.

To add expressions with the same denominators, we add the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{6+10i}{3} + \frac{4i}{3} & = \frac{6+10i}{\color{blue}{3}} + \frac{4i}{\color{blue}{3}} =\frac{ 6+10i + 4i }{ \color{blue}{ 3 }} = \\[1ex] &= \frac{14i+6}{3} \end{aligned} $$

Subtract $ \dfrac{10}{9} $ from $ \dfrac{14i+6}{3} $ to get $ \dfrac{ \color{purple}{ 42i+8 } }{ 9 }$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 3 }$.

$$ \begin{aligned} \frac{14i+6}{3} - \frac{10}{9} & = \frac{ \left( 14i+6 \right) \cdot \color{blue}{ 3 }}{ 3 \cdot \color{blue}{ 3 }} - \frac{ 10 }{ 9 } = \\[1ex] &=\frac{ \color{purple}{ 42i+18 } }{ 9 } - \frac{ \color{purple}{ 10 } }{ 9 }=\frac{ \color{purple}{ 42i+8 } }{ 9 } \end{aligned} $$