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

$$ \begin{aligned} \left( \color{blue}{ 4x+8}\right) \cdot \left( \color{orangered}{ 2x-2}\right) &= \underbrace{ \color{blue}{4x} \cdot \color{orangered}{2x} }_{\text{FIRST}} + \underbrace{ \color{blue}{4x} \cdot \left( \color{orangered}{-2} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{8} \cdot \color{orangered}{2x} }_{\text{INNER}} + \underbrace{ \color{blue}{8} \cdot \left( \color{orangered}{-2} \right) }_{\text{LAST}} = \\ &= 8x^2 + \left( -8x\right) + 16x + \left( -16\right) = \\ &= 8x^2 + \left( -8x\right) + 16x + \left( -16\right) = \\ &= 8x^2+8x-16; \end{aligned} $$

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