Step 1: First we have to write polynomials in descending order.

$$ \begin{aligned} P(x) &= 3x+2 \\ Q(x) &= 4x^2-4 \\ \end{aligned} $$

In this example we are multiplying two binomials so FOIL method can be used.

$$ \begin{aligned} \left( \color{blue}{ 3x+2}\right) \cdot \left( \color{orangered}{ 4x^2-4}\right) &= \underbrace{ \color{blue}{3x} \cdot \color{orangered}{4x^2} }_{\text{FIRST}} + \underbrace{ \color{blue}{3x} \cdot \left( \color{orangered}{-4} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{2} \cdot \color{orangered}{4x^2} }_{\text{INNER}} + \underbrace{ \color{blue}{2} \cdot \left( \color{orangered}{-4} \right) }_{\text{LAST}} = \\ &= 12x^3 + \left( -12x\right) + 8x^2 + \left( -8\right) = \\ &= 12x^3 + \left( -12x\right) + 8x^2 + \left( -8\right) = \\ &= 12x^3+8x^2-12x-8; \end{aligned} $$

Polynomial Operations Calculator