I've always wondered about שלשום. The day before yesterday = 2 days ago. So why does this word have the שורש of שלוש?
The third day before today. היום, אתמול, שלשום. It is a blend of שלוש+יום.
Probably because you've left out the definite articles in English: it needs to be 'The homework was done the day before yesterday.' I suppose you might leave them out if you being very slangy but it's not strictly correct. Mind you, in English you very rarely say 'the homework' - it would nearly always require a pronoun such as 'my' or your', etc., so the sentence is a bit stilted in English anyway.
Just want to point out that 'the homework' sounds odd in English and would very rarely be used. It's nearly always used with a pronoun or adjective, or if not, with a further explanatory clause. So - 'my/your/ etc homework' or'The set homework' or The homework the teacher assigned ...'etc. So the English sentence given as the correct answer here sounds quite odd in English.