How to solve chess combinations ?

The puzzle you posted is in the Advanced section of the "Annihilation of Defence" chapter in the 5th edition of ECC.  Have you tried tackling the Intermediate puzzles?  How do you do on them?

This sacrifice is real which is hardly possible to calculate till the end. Usually such sacrifices are very diffcult to find especially in short time control. It's advanced level for sure and i doubt it's possible to go to it easily.

#39: not full rook. Exchange, and winning a pawn.

#34: If it exists... :P

4th edition i have, i think i should warm-up by finishing an intermediate level combination book first

Lagomorph put it perfectly.  Look for forcing moves - Checks, captures, threats.

1.Rxf6 Exchange sacrifice + 3.Nxf7 Piece sacrifice = Rook down for pawn

But you said "even if the bishop is lost". That's what's I'm referring to.

I found an used 4th edition for free. It wasnt graded by difficulties, and it was only 10th question. So i have no info about difficulty levels.

Yeah then it is exchange for pawn, but can we think it as a winning advantage ? By the way i bought the book you adviced. I only found 1a 1b and 3 books, 1a and 1b was so easy to think about so bought 3rd book, i am not sure if i should start book 2 or 3 but since i couldnt find 2nd book in local bookstore , chosen 3.

It is 1a, 1b, 2, 3, 4 here. Since 4 is endgame book (i already have) I believe you told 1a, 1b, 2, and 3 as 4 levels  ? I bought last combination one (no.3)

According to the author, 2nd book is recommended to a 1600-1700 FIDE rated player and should raise your rating to 200 points more once assimilated. 3rd book, from 1900 to 2100-2200. But who knows, I think it can be taken as a guide to choose what one fits on you, though. Surely you'll find it soon.

Yes, you are right, I forgot to mention 1a and 1b are edited in two different volumes, so there are 5 at the end.

I had gained 1200-1300 and a bad tournament 2 years ago but now its sth like 1570 elo, my best win against 2000, and i have good ratio against 1800+ but i am not sure what is my actual strentgh. I expect something like 1700 since its level i am most comfortable against. But i perform better at solving compared to actual games because sometimes i play impulsive moves cost me points.

last book is endgame book so only 4 books about combinations :)

I think solving problems is a different business, but still a very good exercise. Most of the puzzles in 3rd volume are taken from real games.

So far i got 3, at first one i couldnt found correct candidate move, calculated another promising line, after 10 minutes of calculation (and i was 10 move deep with nothing) i became suspicious about my first move and seen the solution to end instantly, next 2 were easy, 4th seems easy but still couldnt get that down.

If we talk about usefullness, since i started learning chess with endgames 22 years ago, i am better at feeling nuances and crafting plans compared to calculation itself, and i can say i feel the benefit of solving puzzles very much (unfortunately i cant say the same for timed questions like tactics trainer, since mostly i see or guess, only calculate ones with long time allowance)

If you work on your weaknesses you benefit more :) I dont believe anyone can be strong player just by concentrating on 1 aspects of game, but everybody have different weakness so i can improve by practising calculation but you might better analyze some grandmaster games, another should better try to understand nuances between different pawn structures etc. :)

the beginning is difficult but to really learn you must play slow, very slow chess trying to implement the tactics, always keeping in mind that they are there somwhere hidden.