x^(1/2)+y^(1/2)=2 and x+y+4
Have you tried anything at all? Have you, for example, graphed those two functions to see where they intersect. You should have found that they intersect at (0, 4) and at (4, 0).
So x goes from 0 to 4 and, for each x, y goes from $\displaystyle (2-\sqrt{x})^2$ to 4- x.