This was handled oddly and is oddly reported on the Forms 1099-R.
First, if your intent was to roll over $8,000 from the traditional account in the 403(b) to the Roth IRA, the entire $8,000 should have been deposited into the Roth IRA as a direct rollover for which there would have been no requirement to withhold taxes. You then would have paid the increase in your tax liability using other funds.
It appears that they instead did an indirect rollover which requires a minimum of 20%, $1,600 in this case, be withheld for taxes. Why they would do an indirect rollover in-house is a mystery since it makes no sense to do that. However, given that they did an indirect rollover, only $6,400 was rolled over to the Roth IRA and $1,600 was an ordinary early distribution. It seems that they used code 2 for this rollover of the $6,400 because they knew that it went to the Roth IRA. They probably should have reported it as a direct rollover using code G, but the result with code 2 is the same as long as you tell TurboTax that the $6,400 was rolled over ("converted") to a Roth IRA.
The $1,600 reported on the code-1 Form 1099-R represents an amount distributed to you and not rolled over to the Roth IRA, so it is subject to an early-distribution penalty unless within 60 days you used other funds to complete the rollover of the $1,600.
