The battle of bunker hill in 1775 to answer whether the americans would win the war. who the american leader was. how the americans would fight against the british. how the americans would get supplies for the war.

So, the American side lost this battle: because of this I don't think that it showed whether the Americans would win the war: they lost the battle but not by much, so the final outcome was undecided.

Instead I think that it helped to answer "how the Americans would fight".

But I think that the best answer would be that it showed the Americans that they could win: that they had a good chance at winning. Sadly, this is not one of the options.