jmc

Expanding the first product, the distribute property shows that $$(u+4)(u-1)=u^2+4u-u-4=u^2+3u-4.$$The second product becomes $$(u-3)(u+6)=u^2-3u+6u-18=u^2+3u-18.$$Subtracting, both the $u^2$ and the $3u$ terms cancel, leaving an answer of $-4-(-18)=\boxed{14}$.