Multiply $ \dfrac{5}{4} $ by $ 2x $ to get $ \dfrac{ 10x }{ 4 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{5}{4} \cdot 2x & \xlongequal{\text{Step 1}} \frac{5}{4} \cdot \frac{2x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5 \cdot 2x }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 10x }{ 4 } \end{aligned} $$

Multiply $ \dfrac{5}{6} $ by $ 4x^2 $ to get $ \dfrac{ 20x^2 }{ 6 } $.

Step 1: Write $ 4x^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{5}{6} \cdot 4x^2 & \xlongequal{\text{Step 1}} \frac{5}{6} \cdot \frac{4x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5 \cdot 4x^2 }{ 6 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 20x^2 }{ 6 } \end{aligned} $$

Add $ \dfrac{-10x}{4} $ and $ \dfrac{20x^2}{6} $ to get $ \dfrac{ \color{purple}{ 40x^2-30x } }{ 12 }$.

To add 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 $\color{blue}{ 2 }$.

$$ \begin{aligned} \frac{-10x}{4} + \frac{20x^2}{6} & = \frac{ \left( -10x \right) \cdot \color{blue}{ 3 }}{ 4 \cdot \color{blue}{ 3 }} + \frac{ 20x^2 \cdot \color{blue}{ 2 }}{ 6 \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ -30x } }{ 12 } + \frac{ \color{purple}{ 40x^2 } }{ 12 }=\frac{ \color{purple}{ 40x^2-30x } }{ 12 } \end{aligned} $$