First: get yourself a real knife block. Tossing all your knives loose into a drawer is ruining the edges, and keeps them duller than dirt. A dull knife is dangerous.
Second: I wouldn’t bother trying to fix that. The particle board looks like humidity has done a number on it, and it’s falling apart. I would suggest getting a new drawer made out of 1/2" plywood (1/4" bottom) and box joints. It’s pretty easy to do if you have a table saw, but if you’re asking here, I’m going to assume you don’t.
Walks in, assumes you’re stupid, adds nothing, leaves.
On the knife bit it’s no huge deal, it’s not ruining anything, just hone them often. Our knives would get gangbanged all night in the kitchen, they’re designed to have the angle of attack adjusted. - ex chef
Those knives do not look like they’ve been honed since they left the factory.
Every chef I’ve known took immaculate care of their knives, and they sure as fuck didn’t leave them out in the kitchen for everyone else to use.
Also: the value added is in looking at the remaining particle board that’s on the drawer face. You can see that it’s split on the right side, and pieces have separated on the left. That doesn’t have a lot of structural integrity, and gluing it isn’t going to solve that long-term. If humidity is causing the glue holding the sawdust together to lose integrity, then there’s not a lot that can be done that will actually fix the problem permanently. Sure, glue it back together. Then it breaks again, only in a slightly different place. Rinse, repeat. This is the problem with particle board, and why it doesn’t belong in a kitchen or bathroom.
It’s not that bad, glue and screw. Remove the inner board from the drawer front and reattach it to the drawer first. You might have to clean up the MDF a bit. Use filler if you have to, maybe, but don’t use nails. Then reattach the drawer front - again with screws. It might not look perfect, but it’ll probably look fine when the drawer is closed. Consider wood block fillets at the interior corners (sacrificing a bit of space).
Alternatively you could rebuild the drawer frame, using the same drawer front so it matches.
