Ideally you would have opted out of NC tax withholding to allow the entire amount to have been converted to Roth, then made an estimated NC tax payment if needed to avoid a NC tax underpayment penalty. Unless you substituted other funds for the $240 withheld to complete the conversion of the entire $6,000 distributed. Not converting the $240 to Roth means that you did not take maximum advantage of the opportunity to add money to your Roth IRA.
You mentioned that you were doing a backdoor Roth, so if you had a zero balance at the end of 2020 neither the amount converted to Roth nor the amount withheld for taxes will be subject to income tax or to an early-distribution penalty.
You made no Roth contribution. You made a traditional IRA contribution of $6,000. The conversion to Roth is a separate transaction, although the taxable amount of the Roth conversion is determined by taking your basis in nondeductible traditional IRA contributions into account.
