If the $1764 ($1176 plus $588) was withheld from your Traditional IRA funds, then your conversion amount was $8236.
If the taxpayer wants to convert (for example) $50,000 from a Traditional to a Roth IRA, and the taxpayer instructs the IRA custodian to withhold 20% for taxes, the custodian will send $10,000 directly to the IRS and only $40,000 will be converted to the Roth IRA.
If the same taxpayer had requested no withholding, and had paid the taxes from "outside" funds (funds not in the Traditional IRA), then the entire $50,000 would have been converted to the Roth IRA.
In other words, using IRA funds to pay the taxes on a conversion reduces the conversion amount. The amount withheld for taxes is technically considered a withdrawal prior to the conversion.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
