If the joint probability density of X and Y is by
f(x,y) = 2 for x>0, y>0, x+y<1
f(x,y) = 0 elsewhere
The joint distribution is the uniform distribution over the triangle with vertices at (0,0), (1,0) and (0,1) in the x-y plane.
So the probability you want is the area of this triangle cut off by the line y=x/2.
That is it is the area of the triangle with vertices (0,0), (1,0), (2/3, 1/3).