S = {(u,v) =  0<= u <=3, 0<= v<=2}
with x = 2u +3v , y = u – v
1 Answer

You sort of have 4 points to make your image. You of course have more than that, but the maximum and minimum values of u and v are the best choices.
Sketch your graph and plot x and y when u = 0 and v = 0. For this point you just get the origin.
Do the same thing for x and y when u = 3 and v = 0. You’ll get the point (6, 3).
Plot x and y for u = 0 and v = 2 you’ll get the point (6, 2).
Once again for u = 3 and v = 2. You’ll get the point (12, 1).
Connect the dots and shade the region you get and S is any point in the region.