By providing “facility” to someone, you help them achieve their goals in an easier manner. “Facilitate” should remind you of “facility” that makes achieving or doing something easier.
A facile problem is so superficial, simple and docile like a puppy that you are not afraid to face it!
The word “face-tious” should remind you of the phrase “making faces”. People sometimes make faces to tease someone or make fun of something, even in a serious situation!
The word “Fabricate” should remind you of the word “Fibre”. You can use fibres to make a bad weapon or a good thing.
Stale eggs or even un-cooked eggs smell extraordinarily bad, don’t they? The word “egregious” should remind you of stale and un-cooked eggs on someone’s face. Eww!