Multiply $ \dfrac{4}{5} $ by $ x-2 $ to get $ \dfrac{ 4x-8 }{ 5 } $.

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.

$$ \begin{aligned} \frac{4}{5} \cdot x-2 & \xlongequal{\text{Step 1}} \frac{4}{5} \cdot \frac{x-2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4 \cdot \left( x-2 \right) }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x-8 }{ 5 } \end{aligned} $$

Multiply $ \dfrac{1}{6} $ by $ 3x-4 $ to get $ \dfrac{ 3x-4 }{ 6 } $.

Step 1: Write $ 3x-4 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Subtract $ \dfrac{3x-4}{6} $ from $ \dfrac{4x-8}{5} $ to get $ \dfrac{ \color{purple}{ 9x-28 } }{ 30 }$.

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 $\color{blue}{ 5 }$.

$$ \begin{aligned} \frac{4x-8}{5} - \frac{3x-4}{6} & = \frac{ \left( 4x-8 \right) \cdot \color{blue}{ 6 }}{ 5 \cdot \color{blue}{ 6 }} - \frac{ \left( 3x-4 \right) \cdot \color{blue}{ 5 }}{ 6 \cdot \color{blue}{ 5 }} = \\[1ex] &=\frac{ \color{purple}{ 24x-48 } }{ 30 } - \frac{ \color{purple}{ 15x-20 } }{ 30 }=\frac{ \color{purple}{ 24x-48 - \left( 15x-20 \right) } }{ 30 } = \\[1ex] &=\frac{ \color{purple}{ 9x-28 } }{ 30 } \end{aligned} $$