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

$$ \begin{aligned} P(x) &= 3x+4 \\ Q(x) &= x-6 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ 3x+4}\right) \cdot \left( \color{orangered}{ x-6}\right) &= \underbrace{ \color{blue}{3x} \cdot \color{orangered}{x} }_{\text{FIRST}} + \underbrace{ \color{blue}{3x} \cdot \left( \color{orangered}{-6} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{4} \cdot \color{orangered}{x} }_{\text{INNER}} + \underbrace{ \color{blue}{4} \cdot \left( \color{orangered}{-6} \right) }_{\text{LAST}} = \\ &= 3x^2 + \left( -18x\right) + 4x + \left( -24\right) = \\ &= 3x^2 + \left( -18x\right) + 4x + \left( -24\right) = \\ &= 3x^2-14x-24; \end{aligned} $$

Polynomial Operations Calculator