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