We can use distribution property to multiply the polynomial by the monomial.
$$ \begin{aligned} \left( -4x+3 \right) \cdot \color{orangered}{2x^2} &= \left( -4x\right) \cdot \color{orangered}{2x^2} + 3 \cdot \color{orangered}{2x^2} = \\ &= -8x^3+6x^2 \end{aligned} $$