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

$$ \begin{aligned} P(x) &= -4x+6 \\ Q(x) &= x+1 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ -4x+6}\right) \cdot \left( \color{orangered}{ x+1}\right) &= \underbrace{ \left( \color{blue}{-4x} \right) \cdot \color{orangered}{x} }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-4x} \right) \cdot \color{orangered}{1} }_{\text{OUTER}} + \underbrace{ \color{blue}{6} \cdot \color{orangered}{x} }_{\text{INNER}} + \underbrace{ \color{blue}{6} \cdot \color{orangered}{1} }_{\text{LAST}} = \\ &= -4x^2 + \left( -4x\right) + 6x + 6 = \\ &= -4x^2 + \left( -4x\right) + 6x + 6 = \\ &= -4x^2+2x+6; \end{aligned} $$

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