The American Opportunity credit is a credit which directly reduces your tax liability dollar for dollar, in your case by $1,900.
The tuition and fee deduction is a deduction. It reduces your taxable income. In your case, your tax bracket is 12% and the $4,000 deduction will only reduce your tax liability by $4,000 x 12% = $480.
This is why the American Opportunity credit will save you more tax than the tuition and fee deduction.
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