Need help with understanding linked pawn endgame study

I just dont get it. Whatever i move, doesn't work, and i have to move the king backward except forward, completely contraintuitive until the line again doesnt show 0.0 (and the goal is victory!), and even if i uncover every move bye pressing "hint", i will find myself at serious otb in some similar but still different position which i dont really understand so i will drop 1 point...

I would be very pleased if someone explains me that thing once and for all eternity. :)

I don't understand what you don't understand. To create a protected passed pawn you need to passed and ptotected. c4.

(OMG, you are 2150)

try calculating what white will do, and remember to keep the long opposition. I havent seen one of these in my life and solved it bu doing that

There is a mostly forgotten Silman endgame book that devoted a LOT of space to the sort of situation that one would have after ...c4+. I worked through the section and promptly forgot it all, decades ago, but I have a general impression that that sort of thing is harder than it looks with the potential for demanding corresponding-square style maneuvering.

There is a comparatively simple situation that (I think) uses somewhat the same style of thinking. Put white pawns on a5 and c6. Put a black pawn on a6. Put the black king on c8 and the white king on d5. White to move.

1. If White moves to d6, Black MUST move to d8.
2. If White moves to c5, Black MUST move to c7.
3. Therefore, if White moves to d5, Black MUST move to c8.
4. Therefore, if White moves to d4, Black MUST move to b8 or d8.
5. Therefore, if White moves to d4 and from there to c4, Black has no way to remain ready to move to c7 or c8.

NO need to follow the opposition! The king can walk anywhere! You can walk around the entire board!

Well, I dug up my old Silman book. He considered something like this:
White king on e5.
Black king on f8.
White pawn on f6.
Black pawns on f7 and e6.
Black to move.
Apparently, that is a draw, but I wonder if Marraxa has the right position. There does not seem to be the potential for comparable complexities in the Marraxa position if Black simply starts with ...c4+. If it is White's move, dxc5 seems to me to be an easy draw.

I do not understand... Did you link the wrong study? Given you 2000+ rapid rating, this has to be beyond trivial for you.

c4 is the most obvious move in the world, creating a protected passer that can never be attacked.

After that, the ONLY square from which white can defend is pawn is c3, and you can attack it from e4 AND e3, which means that opposition does not mater. All you have to do is step on either of those square and you win.

White as absolutely no way of preventing you reaching these squares because the only thing he could try would be to get the opposition on the 3rd and 5th ranks, but he cannot hold that (even if he managed to get it), because he cannot step to g3 without your c-pawn running.

In other words, the entire solution is c4, and make moves in the general direction of e3 and e4, grab the last pawn, and win... I do not see any way of messing this up (short of not playing c4 of course).

Don't ask me, I am only a woman