Hatch a Duck: Verb, synonym of "take a dump", "make number two", "drop a load", "take a shit".
It is another way of saying you plan on excreting feces from your colon. The word can be augmented in different ways to illuminate the severity of the bowel movement.
"Hey everyone, I'll be right back- I have to go hatch a duck"
"I was in the men's room and I heard someone hatching a ferocious duck"
"I was in the lady's room and I overheard someone hatching a little duck"