Does black have a defense here?

So I've been analyzing all my rapid games lately to look for mistakes to improve on, and stockfish's evaluation of 14. Qxh6 is very confusing to me.

If you follow the engine's recommended strongest moves through 14. ...Bxd4 15. Ng5 Bxc3 16. Bh7+ Kh8 17.  Be4 Kg8 18. Rad1 Nd4 we reach this position, with white threatening a rook lift and an attack that seems unstoppable.

I'm quite new to using the analysis tool on chess.com, so I'm wondering if I'm missing something here. Or if not then how did the engine miss a move that leads to a winning position so quickly?

So after dxe5 the best defense for black is Nxe5. Which leads to 15. Nxe5 Kg7 after which the evaluation is only +1.42 and white seems to have a far less clear line of attack.

Youre getting to caught up in the engine numbers.  Obviously black has other move besides ...Nd5.  That was just one example.

There may also be a bit of the "horizon effect" coming into play here.  You're looking at that final position with fresh eyes and seeing "white threatening a rook lift and an attack that seems unstoppable."  The computer didn't have time or power enough to evaluate those possible lines.  It got to that point as the end of its line and evaluated it based off more static principles.  It saw nothing "obvious" (i.e., no hanging pieces, mate-in-1s, or simple one-move tactics to win material).  It instead saw who had more space/material, whose pieces were more centralized, who had the safer king, and other similar factors and assigned numbers.  Had it more time to go into depth (or if you gave the final position to it as a fresh one to calculate), then it might find that possible attack and change it's final evaluation (as I see it did, evaluating it at 6.39 with the moves played out).

At depth 29, stockfish finally realizes that OP's qxh6 is the better move.  Good instincts Evan, your on your way!  How the heck did the rest of you miss that?

Being serious about the fish changing its mind by the way, it was at move 29 that stockfish suddenly realized qxh6 is in fact the better move by a lot.  Don't see that every day.  

Huh

Interesting, maybe I should go up to a diamond membership then so I can change the depth to 30.

My 2 issues with your post Art:

1. We aren't playing anyone rated 3500+.

2. Using engines and letting them run so long that they will eventually find something that no human ever would,  doesn't seem like a very efficient way of studying.

Just my .02 on this. 

dxe5, is much superior I agree with the engine, first take then get the h6 pawn, also nice attack man  I always attack.

I let it run because it doesn't take very long on my machine, and I never want to post comments without double checking them.  I do sometimes, and sometimes I make mistakes that way, so I like to double check my thinking to prevent falling on my sword.  I just posted the oddity for fun, because its so unusual and unexpected.  The advice to Evan about kicking the defender was perfectly logical and sound, but I didn't think I needed to note that my post was just a fun digression.  Yes, its not really relevant to Evan's desire to learn, but its a rare and surprising thing.  There are clearly some interesting tactical issues buried quite deap.