If you are tiling a standard kitchen backsplash which won’t be receiving frequent soaking showers, you can just tile over the existing drywall, assuming the surface is in relatively good condition.
If you want to do a professional job, use the hardibacker they make a thin one. Liquidnail it to the wall and then secure it with screws to the studs, add fiberglass mesh tape (drywall tape) to the seams and fill the seams with thinset or mastic or whatever you are using to stick the tile to the wall, then install the tile.
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