What's your question? Not particularly easy to figure out the answer, but their explanation is very straight forward. That riddle series on TED-Ed is great. Not sure why there was no 'pause to figure out the answer' for this one.
In a case of 3, person A, B, and C. Assuming we're looking from the perspective of C. I think I understand. That is I make an assumption that I'm not green. So according to my assumption each other one sees one green eyed person and should leave in two nights. When they don't that means my assumption is wrong. Therefore I leave.
Now in a case of four, looking from the perspective of person D I'm having trouble understanding how to say the same thing.