If the cartridge is gray, I'm pretty sure it's fake, DS cartridges are supposed to be black. To tell if a cartridge is fake first, you can look at the Official Nintendo Seal, if your carts are fake, it will say, Original Nintendo Seal Of Quality instead of Official Nintendo Seal, also those numbers on the back, the black numbers, if it's they could be crooked, or not aligned properly, and finally, if you look at the green microchip you might see only one number, but theres supposed to be numbers and letters all along the green microchip.
I hope this helped, and if you can't understand these steps here's a (Youtube) video all about it.