Graphing linear inequalities is not too hard if you know how to graph lines.
x -2y < 6
set x, and y to 0 tfinds the intercepts.
x = 6, -2y = 6 so y = -3.
Those are your intercepts, so connect 6 on x axis with -3 on the y.
finally test a point to see if you are above the line that connects (6,0) to (0,-3).
the easiest is to test the origin (0,0).
0 -2*0 < 6 is true so we note that we are on the origin is part of the solution so we are above the line.