Tile up to the bottom of the cabinets. Period.

You would go up to the range hood/vent. This photo shows a tile pattern above the cooktop.

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im talking about in the stove area... do you

mean ”top” of cabinets? Obviously around the kitchen and everywhere else the tile will go up to the bottom of the cabinets

To the bottom of the vent hood. The purpose of a backsplash is to have a cleanable surface for grease and spatter from the stove top.

You don't have a freestanding hood...so I think to the bottom of the cabinets means to the bottom of where you can see the hood - any visible area between the counter and the upper cabinets. You would not tile on top of your cabinets when they are closed off the way yours are.

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In most cases, you would tile to the bottom of the hood, but the kitchen you show in the photo it doesn't look like you need to worry about that. Just add a backsplash to the open area-see the photo below:

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