Multiply $4$ by $ \dfrac{i}{6} $ to get $ \dfrac{ 4i }{ 6 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 4 \cdot \frac{i}{6} & \xlongequal{\text{Step 1}} \frac{4}{\color{red}{1}} \cdot \frac{i}{6} \xlongequal{\text{Step 2}} \frac{ 4 \cdot i }{ 1 \cdot 6 } \xlongequal{\text{Step 3}} \frac{ 4i }{ 6 } \end{aligned} $$

Multiply $ \dfrac{4i}{6} $ by $ i $ to get $ \dfrac{ 4i^2 }{ 6 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

$$ 4i^2 = 4 \cdot (-1) = -4 $$

Place minus sign in front of the fraction.

Divide both the top and bottom numbers by $ \color{orangered}{ 2 } $.

Add $ \dfrac{-2}{3} $ and $ 6 $ to get $ \dfrac{ \color{purple}{ 16 } }{ 3 }$.

Step 1: Write $ 6 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add fractions they must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{3}$.

$$ \begin{aligned} \frac{-2}{3} +6 & \xlongequal{\text{Step 1}} \frac{-2}{3} + \frac{6}{\color{red}{1}} = \frac{ -2 }{ 3 } + \frac{ 6 \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -2 } }{ 3 } + \frac{ \color{purple}{ 18 } }{ 3 }=\frac{ \color{purple}{ 16 } }{ 3 } \end{aligned} $$