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

$$ \begin{aligned} \left( \color{blue}{ 3x+2}\right) \cdot \left( \color{orangered}{ 2x-9}\right) &= \underbrace{ \color{blue}{3x} \cdot \color{orangered}{2x} }_{\text{FIRST}} + \underbrace{ \color{blue}{3x} \cdot \left( \color{orangered}{-9} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{2} \cdot \color{orangered}{2x} }_{\text{INNER}} + \underbrace{ \color{blue}{2} \cdot \left( \color{orangered}{-9} \right) }_{\text{LAST}} = \\ &= 6x^2 + \left( -27x\right) + 4x + \left( -18\right) = \\ &= 6x^2 + \left( -27x\right) + 4x + \left( -18\right) = \\ &= 6x^2-23x-18; \end{aligned} $$

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