Divide $ \dfrac{2}{3} $ by $ d $ to get $ \dfrac{ 2 }{ 3d } $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{ \frac{2}{3} }{d} & \xlongequal{\text{Step 1}} \frac{2}{3} \cdot \frac{\color{blue}{1}}{\color{blue}{d}} \xlongequal{\text{Step 2}} \frac{ 2 \cdot 1 }{ 3 \cdot d } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2 }{ 3d } \end{aligned} $$

Multiply $d$ by $ \dfrac{2}{3d} $ to get $ \dfrac{ 2d }{ 3d } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Multiply $ \dfrac{2d}{3d} $ by $ \dfrac{8}{3} $ to get $ \dfrac{ 16d }{ 9d } $.

Step 1: Multiply numerators and denominators.

Step 2: Simplify numerator and denominator.

$$ \begin{aligned} \frac{2d}{3d} \cdot \frac{8}{3} \xlongequal{\text{Step 1}} \frac{ 2d \cdot 8 }{ 3d \cdot 3 } \xlongequal{\text{Step 2}} \frac{ 16d }{ 9d } \end{aligned} $$