The nontaxable portion of your $6,000 Roth conversion will be $6,000 * $6,000 / ($100,000 + $6,000) = $340 with the remaining $5,660 being taxable. Your traditional IRA will have $5,660 [Edit: not $5,666] of basis to be applied proportionately to future traditional IRA distributions and Roth conversions.
As fanfare said, to have all of your basis applied requires that your year-end balance in traditional IRAs be zero. The only way to accomplish that now and be able to have all $6,000 of your Roth conversion be nontaxable would be to roll the pre-tax portion of your traditional IRAs back into a qualified plan like a 401(k) in 2022, leaving only the basis in your traditional IRAs. (The tax code permits only pre-tax money to be rolled back to a qualified retirement plan, so all amounts of such a rollover come only from the pre-tax portion.)
