Ă and â are two separate letters. There's no "rule" as to which one it is, just like there's no rule as to when you write x or g. In this case, -ă is a feminine suffix attached to doi, the word for two.
All of the words come from Latin, so you should have no trouble if you speak English because of all of the borrowed loanwords. The word femeie (from Latin familia) is related to family, and doi (from Latin duo) is related to dual or Duolingo.
The word femeie also sounds like French femme or Italian femmina, and doi is related to Spanish dos, French deux, Italian due or even English two.
The right answer was not accepted, perhaps you need to use the word woman in the right order. But there is no order ;)