We can use distribution property to multiply the polynomial by the monomial.
$$ \begin{aligned} \left( -2x+2 \right) \cdot \left( \color{orangered}{-x^2} \right) &= \left( -2x\right) \cdot \color{orangered}{-x^2} + 2 \cdot \color{orangered}{-x^2} = \\ &= 2x^3-2x^2 \end{aligned} $$