OK, I have to admit that I totally made up the name of this opening. If after the moves 1.e4 e5 2. Nf3 Nc6 3. Bc4 Black doesn't want to play the Italian Game (3...Bc5), the Two Knights Defense (3...Nf6) or the Hungarian (3...Be7) and instead plays 3...d6 then I don't know the official name of the resulting opening. It looks a little bit like all of the above mentioned openings, but in reality, it's closest relative would be Philidor's Defense (1. e4 e5 2. Nf3 d6). In fact, this position can be reached via 1. e4 e5 2. Nf3 d6 3. Bc4 Nc6.
This opening can be recommended to the chessplayer who hates to memorize long opening variations (and there is plenty of such long theoretical lines in the Italian Game or Two Knights defense). Probably the only theory you must know is the notorious Legal's mate which, despite it's old age (200+ years!), still appears on a regular basis in club tournaments:
So, if you successfully avoided the above-mentioned trap, then just develop your pieces and grab the initiative whenever possible. A very young Tal did just that in the next game:
Surprisingly, this off-beat opening was played by such great players as Capablanca, Alekhine, Bronstein, Tal, Keres , etc. In the next game the future World Champion created a brilliant miniature:
Two modern Grandmasters decided to check if Alekhine's pawn sacrifice from the previous game could withstand a test of time. As a result, their game was extremely wild!
There is not much theory of this opening, so if you like uncharted territories and new challenges you might want to try the Transformer Defense.