We can use distribution property to multiply the polynomial by the monomial.
$$ \begin{aligned} \color{blue}{5v^3} \cdot \left( 6v-8 \right) &= \color{blue}{5v^3} \cdot 6v + \color{blue}{5v^3} \cdot \left( -8\right) = \\ &= 30v^4-40v^3 \end{aligned} $$