The british army forced the americans to retreat, but sustained heavy losses at:

The Battle of Bunker Hill. Then the correct answer is "The british army forced the americans to retreat, but sustained heavy losses at The Battle of Bunker Hill".

The british initially estimated that the conflict would be relatively straightforward since they outnumbered the colonists and they perceived the inexperienced militias to be inferior in combat. Despite their drawbacks, the americans inflicted heavy losses and, even though they secured territorial gains, the British lost a third of their men in this battle.