Beginner's mistake

I was playing Black. How can I know that d5 is a much better option than h6 in this position? If I play d5, White can play exd6, and I always try to avoid the en passant capture.

Before anything else: in this position there's a mate threat in one move, and that's the real reason h6 loses while d5 saves the game. This isn't a matter of "style" or positional preference — it's forced calculation you have to see.

The threat (if it were White's move): 8.Qxf7#

The queen on f4 already controls the entire f-file down to f7 (f5 and f6 are empty).
The bishop on c4 controls the c4-d5-e6-f7 diagonal (d5 and e6 are empty).
That means f7 is attacked twice and defended only by the king.
If the queen goes to f7 giving check, the king on e8 has no squares: d7 and d8 are occupied by his own pieces, e7 has your knight, f8 your bishop, and f7 itself (the checking queen) is protected by the bishop on c4, so it can't be captured. Nothing can block an adjacent check. It's mate.

[Diagram showing the board with the two attacking lines converging on f7, and d5 highlighted as the key blocking square]

Why h6 loses: h6 attacks the bishop on g5, but that's irrelevant — it touches neither the f-file nor the c4-f7 diagonal. White simply plays 8.Qxf7# ignoring the fact that the g5 bishop was under attack, because mate happens before that matters. This is the classic mistake of "playing the natural move" (kicking the bishop) without first checking what the opponent is threatening.

Why d5 is the only good move: by planting the pawn on d5 you block the c4-e6-f7 diagonal, so the bishop no longer supports the queen on f7. Now if 8.Qxf7+, the king simply answers Kxf7 and White loses the queen for a pawn. On top of that, d5 directly attacks the bishop on c4, gaining a tempo.

The fear of the en passant capture has no basis here. Yes, White can play 8.exd6 e.p., but look what happens next: 8...Qxd6 and you immediately recover the pawn with the queen, which also ends up very active on d6. The net result is equal material, your queen developed, and White's e5 pawn (which was cramping you) has disappeared from the board. That's a favorable trade for you, not a loss. The en passant capture isn't something to avoid on principle — you have to judge the resulting position in each specific case, and here it's clearly good for Black.

The method to internalize: before choosing a "natural" move, always run through the opponent's checks, captures, and threats (CCT) — especially when a queen and bishop are jointly aiming at f7/f2, which is a recurring mating pattern from the Italian Game and related openings onward. If you want, you can verify this line with Stockfish to confirm the evaluation after 7...d5 8.exd6 Qxd6.

@fernandocatolico said in #2:

... [In the position after 1 e4 e5 2 Bc4 Nf6 3 d4 exd4 4 e5 Ng8 5 Qxd4 Ne7 6 Bg5 Nbc6 7 Qf4, 7...d5] is the only good move ... Yes, White can play 8.exd6 e.p., but look what happens next: 8...Qxd6 and you immediately recover the pawn with the queen, which also ends up very active on d6. The net result is equal material, your queen developed, and White's e5 pawn (which was cramping you) has disappeared from the board. That's a favorable trade for you, not a loss. ... If you want, you can verify this line with Stockfish to confirm the evaluation after 7...d5 8.exd6 Qxd6.

I suppose that it is somewhat instructive to ponder how 7... d5 8 exd6 f6 would have been better than 7...d5 8 exd6 Qxd6 or 7...h6, but it would probably be of greater interest to consider how you could have avoided allowing bhem to have an approximately 3.1 advantage by move 7.

The move to give special attention was 4...Ng8 ("(-0.65 --> 0.44) Inaccuracy. d5 was best.")

If (as I hope you will) you continue replying to 1 e4 with 1...e5 and continue going over problems like an approximately 3.1 opponent advantage by move 7, I imagine that, sooner or later, you will notice that ...d5 is often a move to consider.

There shouldn't be much trouble understanding that an alternative to 4...Ng8 should have been sought.
Now, in the comfort of your own home, you can check that you would have been okay after such possibilities as
4...d5 5 Qxd4 dxc4 or
4...d5 5 exd6 Bxd6 or
4...d5 5 exf6 dxc4.
I suppose that it would be a little daunting to try to think through all that in the midst of a 10+0 game. That is why I urge people to prefer 15+10, but, in any event, if you take the time, NOW, to ponder the relevant issues, you will have a better chance of making the right choice on the next occasion when ...d5 is the correct move.

In that position the best move is 1-0 resign
Problem with h6 as mentioned by yourself is you will get mated in 1 d5 stops it temporarily ergo it is a much better move than h6

Yes, the machine indicates that 7...h6 took you from "3.12" to "Mate in 1", and you could have preserved the ~3.12 status of the position by choosing 7...d5 instead of 7...h7.
The thing is that ~3.12 is not all that great for the player of the black pieces. MAYBE, if bhem had made a BIG mistake after 7...d5, you could have saved the game, but you have only a slim chance of surviving an approximately 3.12 disadvantage.
It is valuable if you improve your ability to avoid such a disadvantage in the first place.
In the [Site "https://lichess.org/MwWIL9BA"] game, your position BEGAN to deteriorate when you chose 4...Ng8 ("-0.65 --> 0.44"). Things would have been easier for you if you had managed to preserve your "0.65" advantage, starting with 4...d5.

Your rating is 1000. The main mistake of beginners is to analyze in detail for a long time what does not need to be analyzed.

The best move is 4.d5.

@fernandocatolico said ^

I was playing Black

If you play e4 e5, then you will have to learn a lot of precise moves in a lot of openings.
If you are not ready for this yet, choose other closed openings where there are no fast attacks.

"... You should play the simpler and more adventurous openings, from which you will learn how to use the pieces. Much later on you can go on to the more difficult openings - if you play them now you won't understand what you are doing ... Play the openings beginning [1 e4 e5]. ... if you haven't learnt how to play the open game you won't be able to use positional advantage even if you are able to get it. ..." - Learn Chess by C. H. O'D. Alexander and T. J. Beach (1963)

“... As [First Steps: 1 e4 e5 is] a First Steps book, I’ve tried to avoid encyclopaedic coverage. In any case, you certainly don’t need to remember every single variation and all the notes before playing the opening. Take in the first few moves and the key ideas, and then try it out in your games! ..." - GM John Emms (2018)
https://www.newinchess.com/media/wysiwyg/product_pdf/7790.pdf