What move should I make next?

[Event "Vs. Computer"] [Site "Chess.com"] [Date "2022-08-07"] [White "pawnhub_GER"] [Black "Antonio"] [Result "*"] [Termination "*"] 1. e4 e5 2. Nf3 Nc6 3. Nc3 Nf6 4. Bb5 a6 5. Bxc6 dxc6 6. d3 Qd6 7. Bg5 h6 8. Bxf6 Qxf6 9. Qd2 Bg4 10. O-O-O Bxf3 11. gxf3 O-O-O *

Qe3 Is Recommended By Chess.com In Analysis, Which Makes Some Sense As A Pawn Is Being Threated To Be Taken. By The Way, Your Game Was Going Great Until 6.d3.

#1
After 11... O-O-O white is lost: white loses a pawn and the game. You can play 12 Ne2.
8 Bxf6? is a mistake: you trade your only remaining bishop, a good bishop not on the color of your pawns for a mere knight. You should have saved it 8 Be3.
For that reason also 7 Bg5 was ill-adviced. Better 7 Be3 or even better 7 Qe2.
6 d3 is not wrong, but 6 Nxe5 is more active. It does not win material, but 6...Nxe4 7 Nxe4 Qd4 8 O-O Qxe5 leaves white with better development.

Try different things.

Like that.

#4
No, actually 5 Bxc6 refutes 4...a6. White should capture 6 Nxe5.

Not sure it you are asking about a game in progress, but...

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White can easily take that pawn later.

I guess I play differently than you.

I just don't think saying that move refutes a6 is as helpful as you think, as giving up a pawn in the opening doesn't mean much, especially if you can possibly take it back later.

With the same reasoning giving away a piece in the opening is no problem either, cause you might win a queen later. In the line you're discussing, black gives away a centerpawn, which is a vital pawn. That counts for quite a bit.

A game played by two gms, then, a6 should be played.  He is a beginner.  But of course, since we are supposed to teach him how to play correctly, then maybe your line is better.  So I conseed, that, your move "may" be better, however, that pawn, it looks to me, can easily be taken later.  Why waste time taking a pawn when you can preserve the bishop pair, and cause him to weaken his queenside, so he would be forced to castle kingside?  Since the c3 can't be played it's not the exactly the ruy lopez, but the same concepts occurs.  Though this is not forced, you can see how  things might go wrong for black:

 

In this line black defends the pawn, however, I like white better.  

As you can see it can get bad for black.

 

A single pawn is not the sole outcome of a game in a game for beginners.  It seems you think the opposite.

Ok.

I like black better in diagram 1, because he wins a piece with ...c5, ...c4. In the 2nd example black won't play ...b4 but maybe something like ...Bc5 and black is at least fine. 

It's good that you're thinking about bishop pairs etc. In truth though, 9 out of 10 times material is just more important. Especially for beginners it's more important to learn that it's just not OK to give stuff away, then to learn to come up with excuses when they do give something away. Of course, there are always exceptions, like not taking 'free'  central pawns as black when you're not castled yet. 

Rau4ever, yeah I get it. I thought about what you said. 1 point is enough to win, and one shouldn’t think just because it’s the opening a pawn doesn’t matter. I’ve lost a few games recently with that mentality. Also yeah we should teach beginners how to punish mistakes. I was originally going to say something like, playing d6 is passive, yada yada yada, but yeah, but the fact of the matter is gaining a pawn in the opening is usually a +1 evaluation, so, why tempt fate?

I actually forgot that the bishop retreat doesn’t work in the 4 knights. It’s been so long. I’m forgetting my openings because I have to play against weird stuff at Starbucks. I got caught with a mistake, and I tried to defend it out of reflex LOL.

So false alarm guys.

Resign

#8
"White can easily take that pawn later."
++ That is not the point. I gave the line in #3:
6 Nxe5 is more active. It does not win material,
but 6...Nxe4 7 Nxe4 Qd4 8 O-O Qxe5 leaves white with better development.