Multiply $2$ by $ \dfrac{x}{3x} $ to get $ \dfrac{ 2x }{ 3x } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 2 \cdot \frac{x}{3x} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{x}{3x} \xlongequal{\text{Step 2}} \frac{ 2 \cdot x }{ 1 \cdot 3x } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2x }{ 3x } \end{aligned} $$

Subtract $ \dfrac{x}{9x^2} $ from $ \dfrac{2x}{3x} $ to get $ \dfrac{ \color{purple}{ 18x^3-3x^2 } }{ 27x^3 }$.

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}{ 9x^2 }$ and the second by $\color{blue}{ 3x }$.

$$ \begin{aligned} \frac{2x}{3x} - \frac{x}{9x^2} & = \frac{ 2x \cdot \color{blue}{ 9x^2 }}{ 3x \cdot \color{blue}{ 9x^2 }} - \frac{ x \cdot \color{blue}{ 3x }}{ 9x^2 \cdot \color{blue}{ 3x }} = \\[1ex] &=\frac{ \color{purple}{ 18x^3 } }{ 27x^3 } - \frac{ \color{purple}{ 3x^2 } }{ 27x^3 }=\frac{ \color{purple}{ 18x^3-3x^2 } }{ 27x^3 } \end{aligned} $$