Why does this work?
Use some algebra to prove it.
Let n = the number in the upper left corner of the 2 x 2 square.
Then the other three numbers in the square are represented as follows:
The sum of the nine numbers is
4n + 16 = 4(n + 4).
So, when you divide by 4,
you get n + 4,
and when you subtract 4, you get n (the upper left number).