During which clash, before colonists declared independence from britain, did the american rebels succeed in conquering the british troops they were up against and how? a) the battle of bunker hill b) the battle at lexington c) the burning of falmouth d) the battle of fort ticonderoga e) the attack on quebec

This is a bit confusing. B) The Battles of Lexington were the first fought in the revolutionary war, with more than a year before the declaration of independence. But The Battle of Bunker Hill was also fought before the declaration. 

But the Battle of Bunker Hill was a defeat. So the right answer is B) The BattleS of Lexington. They were won by colonist, due to the use of skirmishing tactics, that did not allow the british regulars to use the full power of their volleys because the colonial troops were scattered and well dug up.