Is there a difference between 'ka'u' and 'ko'u'? Don't they both mean "my"?
In Hawaiian, a-class vs. o-class possessives distinguish between things that you acquire through life (a-class) from things that you were born with, have no choice on acquiring, can get inside of /on top of (like a car).
So in this example, because the bag is something you acquire in life, you would say "kaʻu ʻeke". Things like your name and your parents/siblings would be o-class using "koʻu." Your children would be considered a-class as they were acquired through life. Cars and houses are "koʻu" because you can get inside of them, they are a vessel.
Hope this helps a bit!