This problem is probably one of the worse...
It has a lot of exceptions and cases to handle.
For exemple you could say :
But you can also say :
But, this also works :
And this also :
- J'ai de très gros lapins.(1)
While this also works..
- J'ai des très gros lapins.(2)
Yes I just wrote a sentence where both de and des fit, but actually doesn't have the same exact meaning. (1) uses de to increase the impact of the adjective très gros, while (2) uses des just as a plain article. It would be actually quite hard to explain the exact reason why de or why des on a lot of cases (as a French Canadian) since often we use the one that just "Sounds better".
There are a lot of specific and different cases.
I would recommand you this website that I found searching on google that explains clearly when to use de, des, du, etc.
EDIT : I also wanted to add that, in many cases like these listed, des is used for a little groups, while de is used for big groups.