Homework/class help: Backward propagation of max pooling if each element in an array determines more than one value?

Question

(This isn't actually my homework, and in fact wasn't addressed in my homework, but I was confused about this because my homework hadn't addressed this)

For example if I have an array:

And I do max pooling with:

filter size = 2x2

stride = 1

I get:

If I want to find the derivative from Ln+1 to Ln, I'm not sure what happens to the cell which would have contained the value 6 since it determines the output's center cell as well as the output's top middle cell.

I think I'm probably misunderstanding something about how to solve derivatives if it's connected to two equations.