Try this way of looking at the problem. Draw a sequence of lines each 2/3 inch long starting on the margin of your notepad and alternately labelling them left, right. Draw another sequence of lines just below that, starting at the same margin, each 1 inch long and alternately labelling them left, right. You should see that each LR pair in 4/3 inch long on one row and 2 inches long on the other. You want to know when they next align: in other words, when a mutiple of 4/3 is next equal to a multiple of 2. You'll find that 3 x (4/3) = 2 x (2) so the two are next in step after three double (LR) steps of one and two of the other.