Subtract $ \dfrac{1}{6} $ from $ \dfrac{3}{2x} $ to get $ \dfrac{ \color{purple}{ -2x+18 } }{ 12x }$.

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}{ 6 }$ and the second by $\color{blue}{ 2x }$.

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