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

$$ \begin{aligned} \left( \color{blue}{ 7x-6}\right) \cdot \left( \color{orangered}{ 9x+1}\right) &= \underbrace{ \color{blue}{7x} \cdot \color{orangered}{9x} }_{\text{FIRST}} + \underbrace{ \color{blue}{7x} \cdot \color{orangered}{1} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-6} \right) \cdot \color{orangered}{9x} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-6} \right) \cdot \color{orangered}{1} }_{\text{LAST}} = \\ &= 63x^2 + 7x + \left( -54x\right) + \left( -6\right) = \\ &= 63x^2 + 7x + \left( -54x\right) + \left( -6\right) = \\ &= 63x^2-47x-6; \end{aligned} $$

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