Subtract $ \dfrac{2}{3} $ from $ \dfrac{2}{3x-6} $ to get $ \dfrac{ \color{purple}{ -6x+18 } }{ 9x-18 }$.

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 }$ and the second by $\color{blue}{ 3x-6 }$.

$$ \begin{aligned} \frac{2}{3x-6} - \frac{2}{3} & = \frac{ 2 \cdot \color{blue}{ 3 }}{ \left( 3x-6 \right) \cdot \color{blue}{ 3 }} - \frac{ 2 \cdot \color{blue}{ \left( 3x-6 \right) }}{ 3 \cdot \color{blue}{ \left( 3x-6 \right) }} = \\[1ex] &=\frac{ \color{purple}{ 6 } }{ 9x-18 } - \frac{ \color{purple}{ 6x-12 } }{ 9x-18 }=\frac{ \color{purple}{ 6 - \left( 6x-12 \right) } }{ 9x-18 } = \\[1ex] &=\frac{ \color{purple}{ -6x+18 } }{ 9x-18 } \end{aligned} $$