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

$$ \begin{aligned} P(x) &= 2x+3 \\ Q(x) &= -3x+4 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ 2x+3}\right) \cdot \left( \color{orangered}{ -3x+4}\right) &= \underbrace{ \color{blue}{2x} \cdot \left( \color{orangered}{-3x} \right) }_{\text{FIRST}} + \underbrace{ \color{blue}{2x} \cdot \color{orangered}{4} }_{\text{OUTER}} + \underbrace{ \color{blue}{3} \cdot \left( \color{orangered}{-3x} \right) }_{\text{INNER}} + \underbrace{ \color{blue}{3} \cdot \color{orangered}{4} }_{\text{LAST}} = \\ &= -6x^2 + 8x + \left( -9x\right) + 12 = \\ &= -6x^2 + 8x + \left( -9x\right) + 12 = \\ &= -6x^2-x+12; \end{aligned} $$

Polynomial Operations Calculator