Multiply $10$ by $ \dfrac{d}{4d^2+5d-9} $ to get $ \dfrac{ 10d }{ 4d^2+5d-9 } $.

Step 1: Write $ 10 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 10 \cdot \frac{d}{4d^2+5d-9} & \xlongequal{\text{Step 1}} \frac{10}{\color{red}{1}} \cdot \frac{d}{4d^2+5d-9} \xlongequal{\text{Step 2}} \frac{ 10 \cdot d }{ 1 \cdot \left( 4d^2+5d-9 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 10d }{ 4d^2+5d-9 } \end{aligned} $$

Subtract $ \dfrac{10d}{4d^2+5d-9} $ from $ \dfrac{4}{4d+9} $ to get $ \dfrac{ \color{purple}{ -6d-4 } }{ 4d^2+5d-9 }$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ d-1 }$.

$$ \begin{aligned} \frac{4}{4d+9} - \frac{10d}{4d^2+5d-9} & = \frac{ 4 \cdot \color{blue}{ \left( d-1 \right) }}{ \left( 4d+9 \right) \cdot \color{blue}{ \left( d-1 \right) }} - \frac{ 10d }{ 4d^2+5d-9 } = \\[1ex] &=\frac{ \color{purple}{ 4d-4 } }{ 4d^2-4d+9d-9 } - \frac{ \color{purple}{ 10d } }{ 4d^2-4d+9d-9 }=\frac{ \color{purple}{ -6d-4 } }{ 4d^2+5d-9 } \end{aligned} $$