The r4i sdhc-silver card and the r4i sdhc-dual core card can support the 3ds v6.2.0-12 now.
Follow is the news from official website:
2013-8-10 2013 R4ISDHC Dual-Core kernel updated to wood 1.62.
2013 R4i sdhc-silver Card Supporting the latest 3DS 6.2.0-12 and DSI V2.13 in the world.2013-8-13
After this I think more and more cards will break the block and support the 3ds v6.2.0-x now.
iF you want to download the firmware please click
R4-Download - R4,R4i-R4isdhc the beta r4 card