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

$$ \begin{aligned} P(x) &= 2x-6 \\ Q(x) &= -x+6 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ 2x-6}\right) \cdot \left( \color{orangered}{ -x+6}\right) &= \underbrace{ \color{blue}{2x} \cdot \left( \color{orangered}{-x} \right) }_{\text{FIRST}} + \underbrace{ \color{blue}{2x} \cdot \color{orangered}{6} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-6} \right) \cdot \left( \color{orangered}{-x} \right) }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-6} \right) \cdot \color{orangered}{6} }_{\text{LAST}} = \\ &= -2x^2 + 12x + 6x + \left( -36\right) = \\ &= -2x^2 + 12x + 6x + \left( -36\right) = \\ &= -2x^2+18x-36; \end{aligned} $$

Polynomial Operations Calculator