Translation:After six hours at the airport, František stopped waiting.
how is this wrong? "František stopped waiting at the airport after six hours"
I may be wrong but it seems that there is a different meaning behind the Duolingo translation and yours. You are saying that he stopped waiting at the airport after six hours, assuming that he is no longer at the airport but he could still be waiting somewhere else. He was waiting for 6 hours at the airport, and now he left, and he is waiting at the bus stop, for example. The Czech sentence and Duolingo translation says that after six hours at the airport, Frantisek stopped waiting, but it does not mean that he has left. He may still be at the airport but he is no longer waiting (for someone to show up or for something to happen), he has given up on waiting. In other words, having spent 6 hours at the airport while waiting for something AND having spend six hours waiting for something at the airport can have different meanings :D
My guess is that the Czech for your suggested sentence would be: "František po šesti hodinách přestal čekat na letišti."
In other words, the adverbial phrase "at the airport" modifies the phrase "after six hours", not the phrase "stopped waiting".