In this case, a different word order has a slightly different contextual meaning. The further adjective modifies the part closer to the noun. "nové hezké auto" says to me that he already has a nice car, and now he has another nice car, which is new. "Hezké nové auto" says to me that most importantly it's a new car, which also happens to be nice.
In American English I think it's technically correct but not natural, and in my opinion it's fair for Duolingo to reject such answers.
"auto" does mean "car" but is rarely used on its own like that. It's usually used in noun-as-adjective form, like "auto repairs" or "auto insurance." Occasionally also on signage - for example, I can imagine a sign on a toll booth that says "autos $1.00."
Languages do not work like that. Word to word translation is nonsense. Pretty = hezké Beautiful = krásné In every situation, it could be different and it is just a matter of subjective feeling. Of Course, that both beautiful and pretty should be accepted. But we must learn it the way that creators of this course believe it should be. Of course that in a real conversation, anybody can use what they feel to use and it will not be a mistake.