2x-3y≤0 can be represented by drawing the line 2x-3y=0 (that is, 3y=2x, a straight line passing through the origin and (for example) (3,2). Now shade the area to the left of the line, including what lies below the x axis as well as above it. The shaded area and the line itself represent the inequality.
3x+2y≤6 is 3x+2y-6≤0. Plot the straight line graph 3x+2y-6=0: The x intercept is found by setting y to zero and solving for x: 3x=6, x=2; the y intercept is found by setting x=0: 2y=6, y=3. Draw the line through (0,3) and (2,0). Shade the area to the left of the line. Part of the shading will overlap with the shading for the other line. The shaded area and the line itself represent the inequality.
Where the shadings overlap is the region in which both inequalities are satisfied. That is, all the points in that double-shaded region satisfy 2x-3y≤0 and 3x+2y≤6.