How to make black and white map in cycles and use it as a displacement for bump?

The node setup I gave you has nothing to do with displacement. All it does is mixes two materials using the stencil to determine where each material is displayed.

If you want to put displacement in your scene as well - you need to use the displace modifier on your mesh and assign the same stencil image to the modifier. That will displace your mesh in the same place as your tyre tracks material appears (this part should be exactly the same as the tutorial video).

The advice you were given by Ikari Shingi was sound.

ikari shingi.

Firstly, I didnt say that this is your fault.
And secondly by stencil image i meant the stencil texture, you know it, so dont show off and find niggle in every word of the blender user who just started to learn Blender two month ago.

Moony i understand very well what you are saying but i did use displacement modifier here and i assigned stencil texture to displacement modifier, so on the image you can see real deformation, around the river

I know that displacement modifier has nothing to do with node editor. Its just probably my explanations where not very clear due to the lack of terminology knowledge, but the process is pretty straightforward to me