So I assume you mean 1.e4 e5 2.Nf3 Nc6 3.d4 exd4 4.Nxd4 as other moves, like 4.Bc4, would be the Scotch Gambit.
Black has 2 sound responses, 1 unsound but tricky, and 1 offbeat response that had some hype for a brief while.
The 2 sound options:
1) 4...Nf6 - White has basically 2 options. 5.Nc3 leads to the Scotch Four Knights, which can also arrive via 1.e4 e5 2.Nf3 Nc6 3.Nc3 Nf6 4.d4 exd4 5.Nxd4. The second option for White is 5.Nxc6 bxc6 6.e5 Qe7 7.Qe2 Nd5 8.c4 and now Black can choose between moving the Knight with 8...Nb6 or pinning the pawn with 8...Ba6. You would need to study these lines as they are high theoretical.
2) The other sound option is 4...Bc5, against which White has 3 options. 5.Be3, 5.Nb3, or 5.Nxc6. Against the third one, don't take back. 5...Qf6! And due to the threat of mate, Black gets the piece back without damaging his pawns.
As far as the other two, I cannot give you explanations on how to play them and would advise against using them, but in case you also play the White side, there is:
The unsound 4...Qh4. All I know about this line is White should surrender the e-pawn and gains a bazillion tempi on the Black Queen.
The offbeat line, again not knowing the theory, is 4...Bd6. Ask a Scotch guru as I play the French as Black and when I played 1.e4 as White, it was the Italian I played.
Hope this helps.
What moves can be played to counter the scotch game?