2x + 3y ≦ 12

We draw the graph of the boundary line, which is:

2x + 3y = 12

and all the solutions are the "grid-points" (x,y) above the x axis, 
to the right of the y-axis, and either below or on the line.  These
are called "lattice points".   There are 8 of them as you can see 
from the graph below.  The solutions are these 8 points:

(1,1), (1,2), (1,3), (2,1), (2,2), (3,1), (3,2), (4,1)

  

Edwin