I wanted to see how much the Tuition and fees deduction would be

You cannot directly compare the Tuition and fees deduction (TFD) to the American Opportunity credit (AOC) or Lifetime Learning Credit (LLC). The AOC and LLC are credits against tax owed of up to $2500.  

The TFD is only a deduction from income before tax is calculated.  If you qualify, the TFD is $2000 or $4000 depending on your income.  If you are in the 12% tax bracket, a $4000 deduction is worth  $480 (4000 x 0.12 = 480).

It's the $480 that you compare to $2500 aoc or $2000 LLC, not the $4000.

To get to the choice screen in TurboTax, type> letme <in the search box; then click on "jump to".

The TFD is technically an adjustment to income (an "above the line" deduction and not an itemized deduction). This means it has reduced your Adjusted Gross Income (AGI) and (usually) automatically transfers to the state return. So, for example, if you are subject to  3% tax rate in your state, that's an additional $120 (3% x 4000) tax savings; $480 + 120 = $600 total