Why is אתן wrong? I was under the impression that both mean you (plural) and one is feminine while the other is masculine. Are we assuming that 'children' is masculine in this case?
Sort of. Remember that there are two words for children. This group of children could be all boys, or they might have a couple of girls mixed in. 'ילדות' would be strictly feminine, and 'ילדים' is for both masculine/mixed groups. :)
I believe it's because a mixed group is referred to with masculine pronouns. The female pronoun would only be used on a group that is all female. (In the example sentence we have no outside context, so I assumed it meant a mixed group of children.)
If you have the second word, then you do have context; it ends with ם, so the group cannot be all girls, so the first word must also end with ם.
I think its better to give a little information after correct or wrong answer i cant learn pronouns i just memorize them and after some day i forget them give more information about pronouns and how to use them in hebrew please