A BREACH: A gap/in violation of something. Think security breach, agreement/promise breach, rupture.
TO BREACH: to break open/through. Think breakthrough (business) or breakout (prison), or what whales do.
A BREECH: lower/back part of something (breech birth or presentation), the part of a firearm behind the barrel.
BREECHES: Old-fashioned word for trousers. Knee breeches.