well, you already know how to convert from mixed to improper, so let's simply do the multiplication, as it's very straightforward.
[tex]\bf -4\frac{1}{2}\cdot \left( -6\frac{2}{3} \right)\implies -\cfrac{9}{2}\left( -\cfrac{20}{3} \right)\implies \cfrac{-9}{2}\left( \cfrac{-20}{3} \right)\implies \cfrac{-9}{3}\cdot \cfrac{-20}{2} \\\\\\ -3\cdot -10\implies 30[/tex]
