A(0,0), B(4012,0), C(4012,6018), D(0,6018) determine a rectangle which is union of 4012*6018 unit squares. Determine the number of these unit squares which have a non-empty intersection with AC.

The equation of a line will be 3x=2y. First integer point it will touch will be (2,3). From (0,0) to (2,3) it will cut 4 boxes. You can draw and check.
This process will be repeated 2006 times as we have to reach point (4012,6018). From (2.3) to (4,6) it will cut same number of boxes as it did from (0,0) to (2,3) due to syymetry. Hence total boxes cut = 2006*4