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

$$ \begin{aligned} \left( \color{blue}{ 6x+9}\right) \cdot \left( \color{orangered}{ 4x^2-7}\right) &= \underbrace{ \color{blue}{6x} \cdot \color{orangered}{4x^2} }_{\text{FIRST}} + \underbrace{ \color{blue}{6x} \cdot \left( \color{orangered}{-7} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{9} \cdot \color{orangered}{4x^2} }_{\text{INNER}} + \underbrace{ \color{blue}{9} \cdot \left( \color{orangered}{-7} \right) }_{\text{LAST}} = \\ &= 24x^3 + \left( -42x\right) + 36x^2 + \left( -63\right) = \\ &= 24x^3 + \left( -42x\right) + 36x^2 + \left( -63\right) = \\ &= 24x^3+36x^2-42x-63; \end{aligned} $$

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