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

$$ \begin{aligned} P(x) &= x-3 \\ Q(x) &= -6x-9 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ x-3}\right) \cdot \left( \color{orangered}{ -6x-9}\right) &= \underbrace{ \color{blue}{x} \cdot \left( \color{orangered}{-6x} \right) }_{\text{FIRST}} + \underbrace{ \color{blue}{x} \cdot \left( \color{orangered}{-9} \right) }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-3} \right) \cdot \left( \color{orangered}{-6x} \right) }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-3} \right) \cdot \left( \color{orangered}{-9} \right) }_{\text{LAST}} = \\ &= -6x^2 + \left( -9x\right) + 18x + 27 = \\ &= -6x^2 + \left( -9x\right) + 18x + 27 = \\ &= -6x^2+9x+27; \end{aligned} $$

Polynomial Operations Calculator