I am able to connect to the internet using my 3DS so it doesn’t appear to be a hardware problem. When I try to connect to the online game mode using Mario Kart 7, it won’t let me. It will show a loading screen for a short time and then give an error message 006-0612. Why is this happening and only for mario kart?
This is more than likely caused by a NAT problem on your router. If you are unsure what this is, the short version is that your home network tends to block traffic in certain ways to protect you. You may just need to lift some of the restrictions.
You will need to look up the guide for your router to fix this. Generally having NAT type 2 is good enough to support peer to peer online game modes. Best to check the games manual to see what ports it uses too and open those up.