Best reply against the Italian Game after 3...h6 4. d4? After 1. e4 e5 2. Nf3 Nc6 3. Bc4 h6 4. d4:

[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]
1. e4 e5 2. Nf3 Nc6 3. Bc4 h6 4. d4


What is the best answer to avoid pile up of opponent pieces in the center as black? Especially after Nc3 and 0-0, this position sometimes gets awkward as it's difficult for the black queen to find a suitable square that both defends the king and attacks the opponent.
3...h6 is not a mistake, but it's certainly not the best move in the position.

In the opening, one of your goals is to develop your pieces, and ...h6 doesn't do this. The only point of ...h6 seems to be to avoid the line 3...Nf6 4.Ng5, but this line is not dangerous to black at all. Play can continue 4...d5 5.exd5 Na5, and black will have good compensation for his pawn in this well known line.

The reason you may experience difficulties as black after 3...h6 is because you don't achieve any activity with h6, and you let white take control over the center with 4.d4. This is a Scotch Game / Scotch Gambit where white has the useful move Bc4, while black has the much less useful h6. 

Thus, you should not play 3...h6 as black, but instead either 3...Nf6 or 3...Bc5 as black, which take control of the center and activate your pieces. These openings, the 2 knights (Nf6) and Giucco (Bc5) are very solid openings for black. 

Finally, even though a GM used to experiment with this line, it doesn't mean you should play it. Hikaru has played an early 3.Qh5 before in open games (1.e4 e5), but that doesn't make the move good. If black responds properly, white will have no chance to secure an opening advantage. While Hikaru can outplay many GMs even in worse positions, for non-master players, there's no reason to play a sub-optimal opening that has no surprise value (unlike 1.b4 or 1.g4, which can catch opponents off-guard). Thus, one of 3...Bc5 or 3...Nf6 is what you should do. 

*If you are set on playing 3...h6, then you will have to accept a slightly worse position as black. He has wasted time with h6, and gives white an opening edge. An awkward queen might be one of these problems.