Translation:I must stay home to do my assignments today.
"I need to stay home to finish my homework today" should also be accepted
Ok, this is ridiculous, I speak Chinese and I'm trying to test out of Chinese on duolingo because why not? There is no qualitative difference between "need to" and "have to." Every time it throws a 必须 I am forced to guess between the two. Incredibly frustrating... >:(
Well you'll make a good beta tester then. Just keep sending suggestions every time Duolingo marks you wrong when you know it's actually right. After the DL team enter all your suggestions and the course finally comes out of beta that will be a win for everybody.
"Today I must stay at home to do an assignment.", which is rejected, seems to be a reasonable equivalent for "Today I must stay at home to do my assignment.", the suggested answer for the rejected answer.
There's no explicit possession of the assignment ("作業") in the Chinese text, so I'd not expect it in the English translation.
They're both reasonable really since there's no explicit singular (一个) in the Chinese text either. It's because Chinese doesn't require any of these but English requires either a determiner or that the noun be plural. A determiner could be "a" or "the" or "my", for instance. But you don't need any of those if the noun is plural: "Today I must stay at home to do assignments". And of course plurality is usually not explicitly indicated in Chinese either.
That's one of the reasons many translations are usually accepted. When a good translation is not accepted it's our job to suggest they add it.