If you haven't received it already, you will receive a Form 1099-R reporting a distribution from the 401(k). Unfortunately, TurboTax is unable to handle a split rollover reported on a single Form 1099-R, so you'll need to split it into two for entry into TurboTax, one for the portion rolled over to the Roth IRA (the amount shown in box 5) and the other for the $260 rolled over to the traditional IRA (enter $0 in box 5 of this one).
The $6,000 traditional IRA contribution that you've indicated was nondeductible must be entered under Deductions & Credits and the Roth conversion is reported by entering the code-2 Form 1099-R and indicating that you moved it to another retirement account, that you did a combination of rolling over, converting and cashing out, then enter $6,260 as the amount converted. After entering the Forms 1099-R, click the Continue button on the page that lists the Forms 1099-R that you have entered and be sure to enter the 2022 year-end value of your traditional IRAs (presumably zero).
