in chess, please explain possible responses to white's opening with d4, as black
The most common response for White's d4 Opening is the "French Defense", which starts with 1.e4 and continues with 2.Nc3 3.f4 or 3.d5. The idea behind this move order is that Black will play...Nd7 in an attempt to gain space on the queenside (the side of the board where Black's pieces are located). This allows White to develop their king piece more quickly by playing c2-c4 followed by Nce2-g6.

Another popular response for White's d4 Opening is the "English Opening" which starts with 1.e4 e5 2.Nf3 Nf6 3.Bb5 g6 4.0-0. This variation aims to open up lines for White's bishop while still maintaining a solid pawn structure. 5.d4 is also played but it can be considered less standard than other moves such as 5...dxc4 6.Qxd8+ Kxd8 7.Bg5+.