Multiply each term of $ \left( \color{blue}{x+1}\right) $ by each term in $ \left( x+2\right) $.

$$ \left( \color{blue}{x+1}\right) \cdot \left( x+2\right) = x^2+2x+x+2 $$

Combine like terms:

$$ x^2+ \color{blue}{2x} + \color{blue}{x} +2 = x^2+ \color{blue}{3x} +2 $$

Multiply $x^2+3x+2$ by $ \dfrac{x+3}{6} $ to get $ \dfrac{x^3+6x^2+11x+6}{6} $.

Step 1: Write $ x^2+3x+2 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} x^2+3x+2 \cdot \frac{x+3}{6} & \xlongequal{\text{Step 1}} \frac{x^2+3x+2}{\color{red}{1}} \cdot \frac{x+3}{6} \xlongequal{\text{Step 2}} \frac{ \left( x^2+3x+2 \right) \cdot \left( x+3 \right) }{ 1 \cdot 6 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^3+3x^2+3x^2+9x+2x+6 }{ 6 } = \frac{x^3+6x^2+11x+6}{6} \end{aligned} $$