Well that kind of depends, but the short answer is that no, you would not necessarily be paying ANY taxes for this.

The key to avoiding tax on the conversions is having a zero balance in any traditional IRA accounts on December 31 of the year you make the conversion. If you do this, you aren’t subject to the pro-rata rule responsible for the taxes in question.

If you put $6k into your t-IRA then make the conversion, there wouldn’t be any taxes on that money since you were using after-tax funds and you (presumably) had not claimed that deduction on your taxes yet.