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

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

Polynomial Operations Calculator