Posts: 64,651
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Location: Merryland
I'd try to do it over the tiles. You want your cabinets fastened to the studs so you'll have to find them. Maybe open an outled and slide something through the wall to locate a stud and measure 10" OC from there. Or.. can you access the base of the wall? Maybe pull some baseboard and find the studs. I've never used a stud finder over tile but I'd start there.
You can drill holes in the tile with a diamond drill.
Posts: 1,730
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If aesthetics aren’t a concern, you could put the cabinets right over the tile.
I’d try to use a French clear type system to simplify hitting the studs.
A diamond drill bit and a helper with a squeeze bottle of water are your friends here for drilling the tile and keeping the dust down.
-Mark
If I had a signature, this wouldn't be it.
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Im not sure what you mean by aesthetics?