Would someone explain why this would have been the best move?

I am trying to see what I did wrong, in an attempt to try to correct in the future. I do not understand this move in the analysis. Would someone explain to me why exposing my queen to an attacking bishop would have been the best move?

Please focus only on the move chess.com wanted me to make. That is what stumps me.

1...Ne4 2.Bd8 Ba3+ 3.Kb1 Nc3+ winning the queen.  Its a forcing line.

WOW! I have a ton to learn. Would have never thought that far ahead.  Thank you!

Glad to help.  As great a tool as engines can be.  I also think they instill a lot of bad habits.  The only think you should be using an engine foe is to check for missed tactics, and blunders.  Anything else is a waste of time.

Looking at it some more, it seems like a ton of effort for a swap. Is that taking into account the King pin also?

You're trying to understand something that at the moment is way beyond your ability.  You need to concentrate on the basics right now.  What you dont need to be wasting your time on is stuff like this.  This would be like struggling to understand basic math, and wanting to learn Algebra.  But to be fair I will give you my thought process on the position you posted.

Oh!  Forget all about that "best move" crap.  It wont help your game,and whatever engine the site is using isnt always accurate.  Baby steps is the key to improvement.

If you check the position after 4.Ka1 Nxb5 in the variation in #2 you will see that Black is a piece ahead. Until you get more experience, it can be hard to keep the material count straight when calculating a series of captures!

It took some time to actually find it, and in a real game, I don't think I would've seen it under normal circumstances, unless that had been what I was preparing for.

Just for completeness: After 1. Nxe4, 1... Nxe4 doesn't work because 2. Ba3+ Kb1 3. Qxd1 Bc1 4. Qxc1#.

Thanks again! You really put some thought into this and I appreciate it.

So I need to think harder about using checks. In this case, moving Ba3+ would have put me in a more advantageous position, because I make the K move and I am istill in a safe position.

perhaps you wont mind helping me as well. your second move--Bd8--what is forcing about that? Bishop on g5 moves himself into check (one of several possible) when safe squares are available?

sorry. your 'notes' were under a separate post and i didnt see it.