Multiply $5$ by $ \dfrac{i}{12} $ to get $ \dfrac{ 5i }{ 12 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 5 \cdot \frac{i}{12} & \xlongequal{\text{Step 1}} \frac{5}{\color{red}{1}} \cdot \frac{i}{12} \xlongequal{\text{Step 2}} \frac{ 5 \cdot i }{ 1 \cdot 12 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5i }{ 12 } \end{aligned} $$

Subtract $ \dfrac{5i}{12} $ from $ \dfrac{-4+9i}{6} $ to get $ \dfrac{ \color{purple}{ 13i-8 } }{ 12 }$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 2 }$.

$$ \begin{aligned} \frac{-4+9i}{6} - \frac{5i}{12} & = \frac{ \left( -4+9i \right) \cdot \color{blue}{ 2 }}{ 6 \cdot \color{blue}{ 2 }} - \frac{ 5i }{ 12 } = \\[1ex] &=\frac{ \color{purple}{ -8+18i } }{ 12 } - \frac{ \color{purple}{ 5i } }{ 12 }=\frac{ \color{purple}{ 13i-8 } }{ 12 } \end{aligned} $$