From the read me included with the Update patch:
In order to make your r4i gold 3ds support 3DS6.2.0-12,you need to update your r4i gold 3DS with r4i gold 6.2 patch. Please do as the procedures listed below:
1.Goto
www.r4ids.cn and download the latest WOOD R4 for r4i gold(
www.r4ids.us)
2.Download r4i gold 6.2 patch
3.Unzip r4i gold 6.2 patch to the root directory of your tf card.
4.Get a NDSL/NDSi or a 3DS whose system version is under 3DS6.2
5.Run R4iGold_3DS62_Patch_NDSi_3DS.nds to update your r4i gold 3ds
6.Attention: do not power your ds off during the updating process.
8.Now, your r4i gold 3ds can work on 3DS 6.2.0-12
You can also update your r4i gold 3ds on a NDSL on condition that you can not enter wood menu with your card.
9.Just get a working flashcard(such as r4idsn,dstwo and etc) and boot up R4iGold_3DS62_Patch_NDSL.nds
10.Take out your working flashcard from the NDSL and insert your r4i gold 3ds
11.Press KEY_A and the updating process will begin
12.After updating your card with sucess, your r4i gold 3ds can support 3DS6.2.0-12 now.