"I believe that they have their own project."
Translation:Mi kredas, ke ili havas propran projekton.
Simply because of the use of ke.
I'll try to explain, ke typically starts a new clause with its own subject-verb-object formation. "Mi scias, ke li estas alta" = I know that he's tall. English often elides over this usage, but it does exist in English and many other languages. In my sample sentence there are two clauses; "mi scias" = "I know" and "Li estas alta" = "He is tall" the conjunction ke ties these two together into a complete thought. But li isn't "lin" since it is after the conjunction and the subject of its own clause.
The same goes for "ili" in the lesson sentence.
I do hope that this helps.
2018-10-28 Would I be correct in guessing that your answer was "Mi kredas, ke ili havas ilian projekton"? If so, that would translate as "I believe that they have their (i.e., some other group's) project." This is grammatically correct, but not the correct translation.
To refer to the project belonging to the same group, "ilian" would have to be replaced by "sian".
But this is still not the correct translation, because it would mean "I believe that they have their project" which doesn't account for the word "own". That's where the word "propran" comes in, finally giving us the translation they're looking for.
I confess, I would have translated that as "sian propran". Somehow "propran" all by itself feels incomplete. Would anyone care to comment?