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

$$ \begin{aligned} P(x) &= x-6 \\ Q(x) &= -2x+3 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ x-6}\right) \cdot \left( \color{orangered}{ -2x+3}\right) &= \underbrace{ \color{blue}{x} \cdot \left( \color{orangered}{-2x} \right) }_{\text{FIRST}} + \underbrace{ \color{blue}{x} \cdot \color{orangered}{3} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-6} \right) \cdot \left( \color{orangered}{-2x} \right) }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-6} \right) \cdot \color{orangered}{3} }_{\text{LAST}} = \\ &= -2x^2 + 3x + 12x + \left( -18\right) = \\ &= -2x^2 + 3x + 12x + \left( -18\right) = \\ &= -2x^2+15x-18; \end{aligned} $$

Polynomial Operations Calculator