jmc

Rewrite $x+y\le 4$ as $y\le 4-x$. This inequality is satisfied by the points on and under the line $y=4-x$. Sketching this line along with the $4\times 8$ rectangle determined by the inequalities $0\le x\le 8$ and $0\le y\le 4$, we find that the points satisfying $x+y\le 4$ are those in the shaded triangle (see figure). The area of the triangle is $\frac{1}{2}(4)(4)=8$ square units, and the area of the rectangle is $(4)(8)=32$ square units, so the probability that a randomly selected point would fall in the shaded triangle is $\boxed{\frac{1}{4}}$.