which is correct grammar?

The correct answers are "believe" and "it hears". Having said that, most people would use "they" in the second part (as the two previous responders did). Strictly speaking, "the board" is a singular item, therefore requiring the use of "it". In reality, everyone accepts that "the board" is a group of people and would thus refer to it in the plural. Both are correct, depending on the circumstances. The former is a strictly correct answer, the latter a conversationally correct answer. Hope it helps. Even if it is a year late...

We believe that the board will change its mind once they hear the evidence. I think this is more correct than the other one. Is this your assignment or something well im not really good on grammar but i keep on trying.