I paid over 6,000 dollars on my federal and state return. Then the IRS sent me a letter saying I owed an additional 8400. Why didn't the turbotax software catch this.

"therefore received the recovery rebate credit in error"

@jamzgilz 

If you claimed the Recovery Rebate or Child Tax Credits in error, IRS will not allow it.

This is a common occurrence this year.

Do you have 8400 on line 30?  That is the amount for 6 people 1400x6  (like married and 4 dependents).  

Those are generic reasons why they adjusted the Recovery Rebate Credit on your return. A common adjustment is if you claimed the Recovery Rebate Credit on 1040 line 30 when you already got the 3rd Stimulus payment or reported the wrong amounts.  The IRS knows they already sent it to you. Line 30 is only if you didn't get the full amount or qualify more.

They sent the 3rd Stimulus payment (1400 per person) starting in March 2021. Double check your bank statements and check your IRS account (both accounts if married) to see what they sent you.
https://www.irs.gov/payments/your-online-account