My Oxford dictionary says that afuera and fuera are interchangeable. In European Spanish, fuera is the preference. It also says that these words are adverbs. El exterior would have to be a noun because it is preceded by an article. That could be the reason that afuera/fuera are not accepted as translations.
SpanishDict.com gave this example of afuera: Muchas personas viven justo en las afueras de la ciudad. But they defined "las afueras" as "the outskirts".
But note that with examples of sentences with "afuera" is only used as an adverb and never a noun: https://www.spanishdict.com/examples/outside?lang=en&translation=afuera
To MartynDanc: I don't think so. Its to do with adverbs/nouns/ adjectives. JulianaMiranda says in an above comment "You can't use an article with fuera or afuera". My dictionary gives "Fuera" as an adverb (en el exterior) outside. It gives "Exterior" as an adjective (de fuera) outside, but also as a noun (1)(surface) outside (2) (en el exterior) outside. So I think that Duo is asking for the noun version, "The Outside" and if Juliana is right, and I have no reason to doubt her, it can't be "La fuera".
Take a look at this extension for Duo. forum.duolingo.com/comment/38731989 It is really useful. Once you have submitted your answer it shows you all the alternative answers that would be/could be accepted. Also if you have got it wrong it highlights where it is wrong in your sentence, which will hopefully cut down on the "my answer should be accepted" submissions to Duo. I stress this is not a cheat because the alternatives only come up once you submit your answer.