Education

I am very appreciative of your help and  am willing to accept that answer. But please provide a citation/example that I can reference. No problem there.  From everything I have read, that is not the issue I am running up against.  Take the very simple case below from IRS Pub 970 page 16. Bill used $4000 for qualified education expenses and therefore got a $2500 credit. $1500 of that is non-refundable and $1000 is refundable. Yet he took the entire $2500 credit because he owed $2506 in taxes. So he is claiming all of the refundable portion ($1500) as non-refundable. Correct? What is different in Bill's case and mine? I assume if Bill only owed $2000k in taxes, then if eligible he would get a $500 refund. AND - if not eligible, he would still get to wipe out the $2000k, but not get any refund.

I have included the entire Student Info Wks table and 8863 info below.

Example 1—No scholarship. Bill Pass, age 28 and unmarried, enrolled full-time in 2020 as a first-year student at a local college to earn a degree in law enforcement. This was his first year of postsecondary education. During 2020, he paid $5,600 for his qualified education expenses and $4,400 for his room and board for the fall 2020 semester. He and the college meet all the requirements for the American opportunity credit. Bill's adjusted gross income (AGI) and his MAGI, for purposes of figuring his credit, are $34,900. Bill claims the standard deduction of $12,400, resulting in taxable income of $22,500 and an income tax liability before credits of $2,506. Bill claims no credits other than the American opportunity credit. He figures his American opportunity credit based on qualified education expenses of $4,000, which results in a credit of$2,500 and a tax liability after credits of $6 ($2,506 -$2,500).