Nc3 is the most common way to fight the Modern Defense. We are looking at the Tiger’s Modern setups against, and the Pseudo Austrian Attack and the Two Knights Variation for white.
For an introduction to the Modern Defense, watch this video on the basics: https://youtu.be/slNeLTit2J8
The Standard Line (quite an unimaginative name) is the best response white has against g6, Bg7. White simply develops his knight to the center in the classical fashion and lets black get on with his plans. After d6, white now chooses between three main moves.
4. Be3 is the main and the best move, developing a piece and getting one step closer to the classical chess ideal of having all the minor pieces developed and the king castled. Black’s main response here is the Tiger’s Modern setup characterized by the move a6. It was popularized by GM Tiger Hillarp Persson, who also wrote two amazing books on it. The idea behind the move is to quickly take up space on the queenside with b5, and then continue with Nd7, Bb7 and c5, striking at white’s central pawns.
White can play in several different ways against this, but most often the games are going to be very sharp.
4. f4, the Pseudo Austrian Attack is white’s second most common move. It’s also the most aggressive setup white could choose. It resembles the Austrian attack in the Pirc. The idea is to create a strong central pawn formation which is very flexible and can be used to gain space and to push black’s pieces away. Black will continue with the Tiger’s Modern setup here as well, but it will be much sharper.
4. Nf3, the Two Knights Variation is the least active way for white to play. It often transposes into the Classical Pirc (if black plays Nf6). Black’s best defense is the hippopotamus setup characterized by pawns on h6, g6, a6, b6, e6, and d6. It may seem strange, but it gives black a lot of flexibility and many possible pawn breaks. Black will fianchetto both his bishops and place his knights on d7 and e7, playing only on the first three ranks, but still with a lot of chances for dangerous counter play.
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