If millworkman option is not available to you and you do not have attic space above you would run it along the top of the cabinets and either box it in or cover the space with a large crown or create soffit space. An other option is running it through the cabinets.

Thanks. im actually tearing out the current soffits to run the new cabinets up to the ceiling, so hopefully i can avoid having to put a soffit back in! 🤞

Is it not possible to run it through the roof, since thats the ideal place. In my last house, it was run through the tops of the cabinets, and out the end of the house. It did work fine, and I didnt miss the space, because I never used that upper shelf anyway. I would have had to had a ladder permanently in the kitchen, to use it. I would prefer either through the roof or out through side of the house, rather than put a hole in the rim joist.

"But then to get to the outside of the house I'd have to cut that 6" hole (or 8"?) through the rim joist of the house. Is that ok to do? Is that normal?"

If you can get an engineer to stamp a drawing and get inspection to anoint it, you're good to go.

Ah... that. I sort of forgot about the fact I probably need to get a permit for this kitchen remodel, which probably has to include the venting plan. [I'm not changing any of the walls, just new floors, cabinets, counters, lighting, and the new range hood / venting -- I probably need a permit?] DIYer here.... not quite up to speed on all the rules.