Multiply $ \dfrac{1}{3} $ by $ 2x-5 $ to get $ \dfrac{ 2x-5 }{ 3 } $.

Step 1: Write $ 2x-5 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{1}{3} \cdot 2x-5 & \xlongequal{\text{Step 1}} \frac{1}{3} \cdot \frac{2x-5}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot \left( 2x-5 \right) }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2x-5 }{ 3 } \end{aligned} $$

Multiply $ \dfrac{3}{4} $ by $ x-2 $ to get $ \dfrac{ 3x-6 }{ 4 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{3}{4} \cdot x-2 & \xlongequal{\text{Step 1}} \frac{3}{4} \cdot \frac{x-2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3 \cdot \left( x-2 \right) }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3x-6 }{ 4 } \end{aligned} $$

Subtract $ \dfrac{3x-6}{4} $ from $ \dfrac{2x-5}{3} $ to get $ \dfrac{ \color{purple}{ -x-2 } }{ 12 }$.

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}{ 4 }$ and the second by $\color{blue}{ 3 }$.

$$ \begin{aligned} \frac{2x-5}{3} - \frac{3x-6}{4} & = \frac{ \left( 2x-5 \right) \cdot \color{blue}{ 4 }}{ 3 \cdot \color{blue}{ 4 }} - \frac{ \left( 3x-6 \right) \cdot \color{blue}{ 3 }}{ 4 \cdot \color{blue}{ 3 }} = \\[1ex] &=\frac{ \color{purple}{ 8x-20 } }{ 12 } - \frac{ \color{purple}{ 9x-18 } }{ 12 }=\frac{ \color{purple}{ 8x-20 - \left( 9x-18 \right) } }{ 12 } = \\[1ex] &=\frac{ \color{purple}{ -x-2 } }{ 12 } \end{aligned} $$