"Give a monkey's" is a slang expression meaning "to not care at all" or "to be completely indifferent". It's often used in a negative or dismissive way.
Here are some examples:
* "I don't care what he thinks, I don't give a monkey's!"
* "She's going to fail the test, but she doesn't give a monkey's."
It's important to note that this phrase can be considered rude or offensive, so it's best to use it with caution.