Add $6z$ and $ \dfrac{2}{3} $ to get $ \dfrac{ \color{purple}{ 18z+2 } }{ 3 }$.

Step 1: Write $ 6z $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 3 }$.

$$ \begin{aligned} 6z+ \frac{2}{3} & \xlongequal{\text{Step 1}} \frac{6z}{\color{red}{1}} + \frac{2}{3} = \frac{ 6z \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} + \frac{ 2 }{ 3 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 18z } }{ 3 } + \frac{ \color{purple}{ 2 } }{ 3 }=\frac{ \color{purple}{ 18z+2 } }{ 3 } \end{aligned} $$