"Maybe they have already been waiting for several days."
Translation:Forse aspettano già da diversi giorni.
"Da" means "for" when you want to express a time which ocurred in the past and still continues on the present.
To put it simple:
Everytime you use the structure "for + something + time", you use "da" instead of "per".
We have been friends for seven years = Siamo amici da sette anni or Da sette anni siamo amici
Sorry but I've been given 'stanno già aspettando' as the answer for this and there is NO WAY that this construction has been taught or even mentioned before. I am getting very frustrated by answers that are impossible to get right because they are far more complicated than anything that has been taught.