How to avoid backdoor Roth IRA taxable on NJ return?

On the 1099-R entry, did you follow the data and enter basis (form 8606)?

The backdoor conversion only is "backdoor" because it would be conversion from a nondeductible Trad IRA contribution, done nearly immediately after making the contribution. If this taxpayer had other funds in Trad IRA, SEP IRA or SIMPLE IRA, other than basis, that isn't Backdoor; it's pro rata taxable.

The same is true for that distribution; early means penalty. Did it meet the 5-year qualification? Were there other contributions (other than the conversion), or is that the "same" $6k? Roth distributions have an ordering rule for determining what came out first:

(1) IRA participant contributions, (2) taxable conversions, (3) non-taxable conversions, and (4) earnings. Roth ordering rules only apply when a withdrawal from an account is a non-qualified distribution.

You can review if you checkmarked or otherwise noted everything that applies to each event. Take them separately.

I see this is where they should end: "If you convert a traditional IRA to a Roth IRA, any amount from the existing IRA that would be taxable if withdrawn must be included in your income on Line 20a, Form NJ-1040 or Line 22, Column A, Form NJ- 1040NR. Residents must also report the excludable portion of the converted IRA on Line 20b, Form NJ-1040."