If we are all women, then it would be आयेंगी
what's wrong with आज हम घर आयेंगे?
I also got this marked wrong: Aaj ham ghar aayenge. Is it wrong?
No it's not wrong
Aaj ham ghar aaenge
Ye galat kyon bata raha hai
आज हम घर आएंगे can never be wrong.
Please amend the software input suitably.
I have copied the answer ( input)
to go further on COMPULSION.