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Thanks for your advice. Please suggest whether i understand this right. Thanks so much!

First, both $6000 are non-deductible money. I opened the Traditional IRA really just for the recharacterization and conversion, so there's no deductible money in this IRA account. Do I still need to do 2021 tax amendment? (Yes, I already filed Tax for 2021 and didn't realize i was not qualified for Roth contribution in 4.2022). I looked at 1040-X and did not see any part i can change as both 6000 are post-tax money. 

Second, For 2021 8606, please review:

Part 1:

line 1: $6000 ( not $5500?)

line 2: 0

line 3: 6000, No (it says "in 2021, did you take a distribution from traditional, sep, or simple iras, or make a roth IRA conversion", so i should choose no? because my conversion happed in 2022 although it is for 2021 Roth-IRA back-Roth).

For part 2: if i understand this right, it is for the conversion happened in 2021, so i'm not the case, i should leave it blank. 

and I assume above is what i need to do tax wise and the rest is for tax report in 2023 which i should do 1040 plus 8606 (line 2 will carry the 6000 basis from 2021 and line 3: choose yes; For part 2: line 16: i should do $12000, since i did 2 conversions in 2022 although it's for 2021 and 2022 roth-ira-backdoor roth).

Am I correct above? Thanks so much!