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endgame puzzle + how to start to improve?

im a beginner, and i dont understand (a lot of things of course, +) how to solve puzzles like this:

lichess.org/training/UqUCm

why the solution is the best move (why not a5 for example)? and how to start to improve / think in situations like this (books, youtube) below 1200 point?

thanks in advance.
In King + Pawn endings, look for 1)passed pawns and 2)opposition.

1) Passed pawns : Because they will go for queening square.
2) Opposition : Because You need to go inside your opponent's camp to eat his pawns, because no passed pawns exists, so by eating some pawns, a passed pawn will be created.

So, h4 is the right and only move. As no other move exists for white, so of course he has to move his king, and then Black's king will penetrate, and take white's pawns. Try play this position with computer, and you will understand better.
@pythonprof - Playing a5 will allow white to take en passant and get a queen. Best move is h4, black's king maintains opposition and will be able to get behind whites pawns, when white moves the king one way or the other. If you don't understand the terminology used here... Try taking the Lichess basic chess course: - lichess.org/learn - After you complete the basic chess course, Do the Practice course -lichess.org/practice - It will do wonders for your game. :]
#2 And in this position, you will have to penetrate with your king to get a passed pawn. So, oyu use h4 as a reserve tempo. White's king will give way and Black can take the queenside pawns.
I think the above statements kinda explained this puzzle particularly. I just wanted to add some related comments.

Ultimately, a lot of endgames come down to tempo and pure calculation. You should study the basic endgames like K & Pawn endgames, and kinda move up from there. There are multiple types of endgames, such as king & rook & pawn vs King & rook, that can be made a draw or a win based on the person with the endgame knowledge.

There are plenty of endgame studies on lichess, and plenty of guides on youtube to help you get started with these positions. Endgames are the most important part of chess, as if you don't know how to use your advantage, then you can't really hope to win even if the middle game and opening got you there.
Πόσο μαλάκας είσαι απ' το 1 ως το 10;
I'll add another thought...

After the puzzle, you can see a link to the actual game. I'll often go to the game, and then send the PGN and the move number to Evernote if I do not understand the solution.

I'll then be able to bring up the exact position later and play through the variations with my engine to help understand why my solution didn't work and the solution given does.

I really like this ability in lichess. I want to be able to look at my failed attempts and understand why I failed. :)

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