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:
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.