It's a linear function, so it will be maximized on the boundary; specifically at one of the vertices when the bounary is a polygon. Write the first two inequalities as equations in intercept form:
x/6 + y/9 = 1 . . . . divide by 18 to get x-intercept = 6 and y-intercept = 9
x/4 + y/3 = 1 . . . . divide by 12 to get x-intercept = 4, y intercept = 3
The >= direction of the 2nd inequality, and the fact both intercepts of the second boundary line are inside the region defined by the 1st inequality, make it easy. All corners of the boundary are on the axes. Evaluate the function at (6, 0), (0, 9) , (4, 0) and (0, 4) to find the maximum location and value. I get f(0, 9) = 63.