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

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

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