Can you find the studs? If so, measure from there to find another stud, etc. Drywall (sheetrock) is not strong enough to support hung cabinets.

Or horizontal blocking attached to the studs.

no studs we can find 🤷🏼‍♀ what now?

As the others have said, you need to find the studs. In older houses, the studs aren't necessarily equally spaced, so while measuring over from one stud to try to find the next might put you in the right area, it isn't a guarantee.

One method I've used with success is to drill a small hole in the wall. Then insert a bent coat hanger and twirl it around. If it hits a stud, then you can figure out where the stud is based on how much you had to turn the coat hanger.

Once you find the studs, you'll need to use extra long screws to get through the drywall, plaster, lath, and far enough into the stud.

Or just cut holes in the wall and find the studs. You can just rough patch it afterwards since it'll be hidden behind the cabinets anyways.

You absolutely have to attach to studs, solid blocking or plywood with substantial anchors. Otherwise in short order you will have a pile of broken cabinets and dishes on the floor.

Open the wall if you to. You can't hang cabinets on sheetrock and lathe. Are you hanging kitchen cabinets? I say this with all sincerity and without snark--are you sure you're up to the task? You may need to call in professional help. It sounds as though you've already attempted to hang kitchen cabinets in sheetrock and watched the sheetrock fail. You probably already have some holes in the walls. Open one up until you find a stud and then sort out how far apart the studs are and go from there.

thank you all

Not all old houses have studs. Not a single one in my house, it's plaster over triple wick brick. Also instead of cookie cutter cabinets you could use free standing full height cabinetry, they need to be anchored to walls but a less destructive than modern ones. That's my plan when I redo my kitchen.

If the wall is brick or concrete behind the plaster and drywall, you can still fasten the cabinets to it but you need to securely anchor it into the brick/concrete using appropriate fasteners (and enough of them).

I think all old wood-frame houses have studs, otherwise what would they have attached the lath to? I've never lived in a brick house and everything I know about hanging cabinets on a brick wall I just learned from Greg, above.

Studfinders don't work at all well on lath and plaster walls. I usually use the tapping and listening approach (which the extra layer of drywall will probably make less effective). Even so, I've drilled many a hole in my walls expecting to hit a stud and instead hitting air.

@cawaps, the issue is that she may indeed not live in a wood-frame house. I didn't consider that at first, but that's the point that's being made.

I do live wood-frame house but thank y'all for the advice

It could be just plaster directly on brick (no lath). But then what would the drywall be attached to?

Or it could be furring strips attached to the brick and the lath/plaster on that (and the drywall also screwed to that).

But the bottom line is that the OP needs to figure out what kind of wall they have before we can help further. Cut it open and find out! :)

(I posted this before seeing the last post by the OP)