Training puzzles, methods. How is this endgame a win?

https://lichess.org/training/knightEndgame/FR9j6
I resolved the puzzle, the machine sacked the knight
because the king dominated it, leaving it no room to
escape and play on the board, but Its not clear to me how
a real game will develop, trying to be spot on I would say
the simple idea of the position, Its that white
has a superior knight because its free at the board and
can move with no impediments, its not blocked as its
the case of black's knight.
However a game, Its not just about 2 or 3 correct moves
but about a series of good moves until checkmate or the resignation of your opponent, this puzzle gives me the
opportunity to highlight the difference between winning
a puzzle and winning a game,
therefore this important because in our training season
What do We want? Do de want to do a lot of puzzles?
Do We want to win a lot of points with them, that is
winning the puzzles? or do We want to understand deeply
the position?
because in my opinion I see two big ways of training puzzles,
two methods, Im sure there are more but I only see two now.
First method, Its to do lots of them, like trying to
win the puzzle fast and get an advantage, I will say
about 30 seconds, a minute by puzzle by average normal
player (top bullet players are the exception, not the rule...)

The other method, its to understand the position,
here the aim Its not just to win the puzzle but to get
a rather full understanding of the position,
What do I mean by this? Exploring 2 , 3 or up to 4 lines
in the puzzle, and once is done think about its continuation
towards the endgame, how to trade and win the game,
create another weakness or get another advantage,
Ok so these are my thoughts of today, my early thoughts
about puzzle training, I did puzzles in the past, but I did not
think them.

Back to the puzzle position, (first line of the post)
is anybody able to win it? or find an easy shortcut?
I did not think much I just saw white could locate his
white knight on c3 to attack two black pawns but the
black king can defend them, so give me a moment
or collaborate if you want...

Ifblack does notplay f6, black will have a potential
knight e5, knight c6, knight AI attacking the black pawn...
I think
Maybe later h5 becomes a weakness
Knight e5, knight g7, knight h5

Are you asking what makes the position a win? Or are you asking for a change to the programming? Need clarification.

The win of the game after the computer moves from the puzzle relies on zugzwang - making black have no good moves. Once your knight attacks the pawns from c3, the black king must sit only on c6 to defend them both. In that stuck position, black must move only his pawns, which make them vulnerable to attack and also allows the white king to enter the position to win.

Ok, yes then I "almost" resolved it, I did not come with
the zungwang finish, thanks @DrHack
I guess my question is a question of precision
whether should be a guess or a calculated finish deep
in the line, because I think I have the bad habit
of
getting the puzzle right without calculating the full line.
Yes Its Zugwang because only the c5 square defend the b5 square and the d5 square (not c4), I think there is a difference between resolving a puzzle and studying it,
perhaps by writing your puzzle thoughts, It gets better
stamped, in your memory my two cent....
and you get confidence in the position instead
of rumble and rumble and fussle and fussle...

My vision and finger skills are rudimentary,
I like blank spaces.

Zugzwang puzzles are great to create new awesome
neat studies, I get a lot of inspiration between the
relation flow of zugwang to checkmate.
The first step is to put your opponent in zugzwang and the
second to put the opponent in checkmate, but
a zugzwang its not a checkmate although It has similarities
due to the lack of space.

Next puzzle,

Here the idea is to be patient and pay attention to the
board, if the puzzle its too obvious It may be a trap,

The following question arises, Its white' s turn to play,
is there any chance white can lose a game if he is going
to win a queen, but as usual chess Its a game of fireworks
and surprises and the best thing is to not get things
for granted but to calculate them, but here We find two
paths the simple calculation and the calculation of ideas
and both are needed, so the theoretical question goes like
that: in what circunstances can white go wrongly if
the white player is going to grab a queen,
and the answer is as following:
Chess is a game of material, the only thing more important
that material its the king, the only piece more important
than the queen is the king,
so we focus here in the top four pieces on the board,
these pieces are the two queens and the two kings
This is important, but back to the simple calculation
of the position, what is the hindrance, the danger of
getting a queen? And We get a simmetrical answer
We can lose our queen as well, because at the board
there can be more than one tactic in diffetent squares
So instead of winning a queen, his queen and losing
our queen, We can be more aggresive and defensive
at the same time, our weakest link the queen needs
to be protected and become a weapon
So instead of an evaluation, a roallercoaster evaluation
winning opponent queen, losing our queen about
equality , We have an astounding position,
We want to reach a superthreat we threat and checkmate
at the same time, checkmate on h7 and since
the opponent has one turn to move and We have two
main threats instead of zero, We will get the queen.
So We see that Its easier to play the board than to explain it
because its very rocambolesque, I made that up.
Pieces are like chains of thoughts and maneuvers very
difficult to describe with my simple standart english.

I forgot to mention Ne2

The key is to not think abou tactics but to think
about the position, remember than first and foremost
the puzzle is a position of a chess game ( not a special
study, antichess, strange pieces...)

When we play a puzzle we have the mental disadvantage
that It is not our game, We did not played the game,
We did not develop the pieces, and Its very easy to be
biased, think without looking that the position is equal
like in a standart chess game, move 1 equal material
Sometimes one can fail a puzzle because he is concentrated
in the minor pieces, in check, checkmate, the queen...
but one side can have a pawn mayority of five pawns
versus the other side three pawns,
so Why is this fact important?
Because in a puzzle there are a lot of tactics and combos..
and the mistake can be to go for a superior exchange
a rook for a knight, for example, winning a rook and losing
your knight but here lies the CLUE
A TACTIC IS NOT A POSITION
What does it mean? That a tactic is a part of the board,
a fragment of the total position, and CHESS is about
playing the position not the tactic, because in the position
can be multiple tactics, and many times its necessary
to choose the best tactic so that the total material
of the position, its evaluation its enough,
so It goes like that the appearance of a good move
can be a bad move if you do not get enough compensation
by not playing the best moves.
Lets try to explain this again because Its very interesting
and important,
A CHESS POSITION CAN HAVE MULTIPLE TACTICS
Ok, but this is not enough
SOME TACTICS ARE BETTER THAN OTHER TACTICS
A tactic is a component of the position, the aim of chess
Its not to win tactically but to have a better position
but this is very hard to understand because Its usually
the same, the trick, the mistake is that a good tactic
can give you a bad position, for example if you get a +2
and you need a +5,
so why does this happen? Because in the turn you can have
positive evaluation, while at the same time in the total
score evaluation of the position, you can be under zero
So We need to differenciate between:
INCREMENTAL ADVANTAGE BETWEEN TURNS and
OVERALL ADVANTAGE OF WHITE VERSUS BLACK OR
BLACK VERSUS WHITE.

We aim for the second not the first in every chess position
including puzzles, It was hard to find good words to
explain that, Its very few concepts but they need to be
finely grasped, interiorized.
Ok, bye