I think they chose the Spanish sentence such that it would not have to be in Subjunctive mode which is probably not introduced at this point in the tree yet.
The "I don't think it's possible" corresponds to "No pienso que sea posible" which would be much more natural in Spanish as well.
To me it reflects a difference in the level of certainty. "I think it is not possible." means that is my firm belief. "I don't think it is possible." to me reflects less confidence.
Change the word "think" to "know" and it illustrates the point: "I know it is not possible" - very definite! "I don't know it is possible" - reflects doubt.
Yes, but the "that" in "that is not possible" is not the same "that" that is a translation of que.
"Que* translates to "that" in sentences like "I know that he is there", or "I like the gift that you brought". It's a conjunction, not a pronoun.
In your sentence that would translate to eso, ese, or esa depending on the context.
Actually, yes, it does work pretty much the same. It depends on whether your sentence (in English) is "I think (that is not possible)" or "I think that ( [something] is not possible)". The second one is the correct translation of "que" in this case, but it is missing a subject for the clause.
The point is that if anyone said 'I think it's not possible' (certainly on this side of the pond), they would immediately be identified as a non-native speaker by native speakers, however correct the sentence is, as it simply is not in common useage. Any English learners wishing to 'blend in' with British locals would be best served by sticking to 'I don't think it is possible'. I am currently learning Spanish from my friends and neighbours while living in Spain, as well as using Duolingo, and while Duolingo is an excellent tool, it doesn't always accurately reflect the language as used in the part of Spain where I live. Ultimately, I would rather use the 'living' language than textbook Spanish, and there may be Spanish speakers learning English who would prefer to do the same, hence my advice above…
Your sentence is equivalent to:
"I think (that) that isn't possible."
Thus, your that in that sentence is a translation of eso or aquello. In other words, your sentence is the translation of:
"Yo pienso que eso no es posible"
The other possibility is like @DavidMoore622957 said that you forgot to include the implied it (if we take your that as a conjunction instead of the subject)
I hope this has been a grammatically satisfying answer.
Not exactly the best way to learn a language, you think? More important to realize why DL didn't accept your answer, otherwise you're just repeating like a parrot.
In your case you used "that" when that word isn't in the Spanish sentence at all. Your sentence would be "Yo pienso que esto no es possible."
There's a small difference between what you tried and the more "literal" translation. See the comment from Johngt44 in response to MoyraWALKER for more information.
Apparently, Duo still rejects "I think that IT is not possible" as well. So, clearly the database of acceptable translations is not complete yet.