The 10K 'claimed for credit or deduction' is for qualifying for the American Opportunity Credit.
per Expert @DavidS127:
"Note that when you have a 1099-Q (529 plan) distribution and someone on your tax return is also eligible for other education credits (such as the American Opportunity Credit or AOTC) there is a screen in TurboTax where you are asked to "allocate" education expenses to those credits versus the 529 plan distribution.
Generally, it is best to allocate enough (but only enough) to these credits first, with the remaining education expenses applied against the 529 plan distribution.
That allocation between education credits and 529 plan distributions can also be done in the Forms mode of your Download/CD version. Go to Forms mode and find the applicable "Student Info Wk".
Scroll down to Part VI and find line 17. If you enter $4,000 on line 17, TurboTax will first use $4,000 of your qualified expenses for the education credits/deductions (e.g., AOTC) and then use the rest of the expenses you entered to apply against the 1099-Q (529 plan) distribution. If you enter zero, all the expenses will be allocated to the 529 plan distribution."
Click this link for more discussion on Allocating Education Expenses.
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