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

$$ \begin{aligned} \left( \color{blue}{ 2x-3}\right) \cdot \left( \color{orangered}{ x-4}\right) &= \underbrace{ \color{blue}{2x} \cdot \color{orangered}{x} }_{\text{FIRST}} + \underbrace{ \color{blue}{2x} \cdot \left( \color{orangered}{-4} \right) }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-3} \right) \cdot \color{orangered}{x} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-3} \right) \cdot \left( \color{orangered}{-4} \right) }_{\text{LAST}} = \\ &= 2x^2 + \left( -8x\right) + \left( -3x\right) + 12 = \\ &= 2x^2 + \left( -8x\right) + \left( -3x\right) + 12 = \\ &= 2x^2-11x+12; \end{aligned} $$

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