Flouting vs. Violation
Here is an example of flouting the maxim of quantity. Diane, the reporter on the Quahog news network is introducing her co-worker who is doing a story in the field.
Diane: And now to Asian reporter Trisha Takanawa, who filed this report... all by herself!
The maxim of quantity is flouted by the addition "all by herself!" The tone is also important but we won't discuss it here. The last bit of Diane's statement is completely unnecessary in the introduction of Trisha Takanawa but she adds it to express something about the intelligence and professional ability of her co-worker. She deviated from the preferred (most efficient) utterance in order to encode more information in what she was saying.
Here is an example of violating the maxim of quantity. Lois had been trying to get Peter to go to the doctor and now she is inquiring about the scheduled visit.
Lois: Hi honey. How was your physical?
Peter: Good. Good. Good...yeah, yeah. Too good, in matter of fact. You know
what the doctor said? Doctor said I was too healthy. You know? In too good of
shape. Don't even know how. Too good of shape.
Lois: You didn't go to your physical, did you?
Peter: No. Ahm, I did not.
She knows he's full of it b/c he tried to give more details than she asked for. He did this not to enrich his communication but to lie. So he also violated the maxim of quality. If the listener is not meant to catch the flouting then it becomes a violation.