Home Improvement

I would not. 6cm is about 2 1/2 inches and I would not rely on a wall framed any less thick than 4-by (3.5 inches). Thinner means more flexion which will lead to problems of your plaster cracking and cabinet flushness issues. In terms of strength, it's probably okay, assuming you have fastened that framing solidly.

The trick to finding your studs is to pre-mark your plaster board and keep transferring those marks outward up to the point of hanging your cabinets.

This will do the trick https://www.homedepot.com/p/NewAge-Products-48-in-Cabinet-Hanger-Wall-Rail-Small-80000/315626565?irgwc=1&im_rewards=1&cm_mmc=afl-ir-2003851-1420157-bing&clickid=XNCxlLRoJxyPU8hUtl209w5pUkH1e6U3JRDVSA0

~~My advice? Knock that "wall" down and pay a proper carpenter to build a proper one. Your studs are too small, they don't go all the way down, you have no room for insulation, and if you try to hang cabinets on that thing, you're going to kill someone when the whole sumbitch collapses.~~

My bad, I didn't know what I was looking at. See OP's diagram to learn more about this, and ignore my ignorance.

This looks like a disaster waiting to happen

Are you getting this work inspected by anyone?

That work, while precise, would not meet code where I live.