Platinum Mincross

2017 February Contest, Platinum: Problem 1. Why Did the Cow Cross the Road
http://www.usaco.org/current/data/sol_mincross_platinum_feb17.html
I was reading the solution to the problem, and I simply could not understand
“Now, let’s consider what happens when we move one cow from the end of the line to the beginning. Suppose this cow ends up in position P in the second line. Since this cow is the last cow in the first line, we can see it contributes N−P intersections. Moving it to the beginning would then contribute P−1 intersections. So moving it from the first position to last position would change the number of pairs by (P−1)−(N−P).”

How do you move a cow from the end of the first line (basically the first field) to the second line (second field)? Don’t you cycle them independently?

I don’t see where they say that they move a cow from the first line to second line.

“Now, let’s consider what happens when we move one cow from the end of the line to the beginning. Suppose this cow ends up in position P in the second line. Since this cow is the last cow in the first line, we can see it contributes N−P intersections.”

Here’s a hopefully more understandable version.
“Now, let’s consider what happens when we move one cow from the end of the first line to the beginning. Suppose this cow is in position P in the second line. Since this cow was the last cow in the first line, we can see it contributes N−P intersections.”