Translation:I must stay home to do my assignments today.
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"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.