"There are two doors in this room."
It is absolutely 戸が二つ, also as already pointed out, 戸 denotes a Japanese style door, whereas the common word is ドア.
Yeah I ageee and this is confusing.. can someone explain why "とが二つ" is a more correct choice over "二つと" ? All the other examples mark me wrong for the latter
It's just how it works. If you want to flip it (counter first) you can use の (i.e. 二つの戸).
と（戸） is a word used especially fot Japanese style doors. It's also the second kanji in Kobe (神戸)!
I think it should be accepted. Report it if it’s marked wrong because the construction «Number + Counter + の + Word» is acceptable as well.