With LED 4" at 3k I would probably do 4 on a dimmer.

Typically a recessed light will not provide the light you are looking for in a closet (does not throw light to the side for the top shelf), and the better (opinion based) aesthetics of a recessed is not maximized in a closed small possibly messy closet.

Also, be aware of newer NEC requirements that the fixture must be enclosed, so like a flush mount (surface) or lens on recessed.

Thank you for the help! Also, what about a 11 by 12 rooms, how many should I have? 4 vs 6 inches recessed lighting?

The amount, placement, and style of fixture should be based on the room function, design, and level of the house. For instance, an 11x12 kitchen has very different requirements than an 11x12 office or 11x12 bathroom. 6" would typically require less fixtures and different spacing than 4", and is usually cheaper and less aesthetically pleasing to many people. And a basic grid of lighting is not the default solution for lighting.