While it's pretty obvious that the R4 doesn't support SDHC cards (at least the original R4 doesn't), the card reader that came with it does indeed support SDHC. I don't know if this has been tested, but I confirm it.
I got my DSTT in the mail today and it didn't come with the card reader (it was the new version from DX), so I inserted the 4 GB SDHC Kingston MSD card I ordered alongside it into the R4's card reader, and lo and behold, it recognized the card. So I downloaded the kernel, got some games running to see if it would copy and it did. Inserted into the DS, booted it up, and I was playing.
So...yeah, for those who thought it didn't work, it does. So you don't need to go and buy another card reader when the R4's will do the job, if you have one already.
I got my DSTT in the mail today and it didn't come with the card reader (it was the new version from DX), so I inserted the 4 GB SDHC Kingston MSD card I ordered alongside it into the R4's card reader, and lo and behold, it recognized the card. So I downloaded the kernel, got some games running to see if it would copy and it did. Inserted into the DS, booted it up, and I was playing.
So...yeah, for those who thought it didn't work, it does. So you don't need to go and buy another card reader when the R4's will do the job, if you have one already.