Oh Yeah, I remember this opening. This is the Scotch Gambit White pretends to be a Moron Variation.
Game Analysis
4 .... Nf6 allows white to play 5 Ng5 threatening Nxf7 forking the queen and rook. It could have gone something like:
5 Ng5 pd5 6 Nxf7 Kxf7 7 Bxd5+ Nxd5 8 Qh5+ pg6 9 Qxd5+
and white is safe to castle while black's king is already out in the open. If the queens trade white has an open file to begin his attack with his castled rook.
4 ... Be7 or 4 ... p h6 would have prevented all that.

4..Nf6 bla
cks best response bowanza the line you gave leaves white down a piece with no attack8...Qh4 was a mistake best is 8...bxc6
11.Be3 and white should win easy
But nice checkmate

Yes 4...Nf6 is a perfectly good move, and most sides moves are fine until the 8...Qh4 blunder. Instead of 7...Bd7 there is a sharper line with 7...Bc5, when after 8Nxc6 black can play the 8...Qh4 idea. Sometime back a strong correspondence player Mark Morse, wrote a "Hard chess" column called "Lost variations" about this. Think can still find it with a bit of gooling.
With 4. ...Nf6 my idea was to transpose into the Classical Variation of the Two Knight's Defense. The usual move order is 1. e4-e5 2. Nf3-Nc6 3. Bc4-Nf6 4. d4-exd4. After Ng5 I would have played Ne5, defending the f7-square and attacking the Bishop.
I still think 4... Nf6 is weak. Look at this variation:
5 Ng5 d5 6 pxd5 Nxd5 7 Qf3
what can black do now? He can't play 7... Qxg5 because 8 Bxg5. Meanwhile his knight on d5 is treatened plus there is a mate threat on f7. I wouldn't want to be in black's shoes.
fine? I gotta admit 7...Be6 is a pretty good move, as it stops mate and saves the knight.
But
if 7 ...Be6 then
8 NxB6 pxb6 and white has an good game. He could trade in the center if he wanted, leaving black with doubled pawns. Meanwhile, his king is safe and prepared to castle while black will probably have to castle long.
This was my first game on chess.com. I was hoping to get some feedback from some more experienced players to see what I could have done better. Thanks.