I'm not sure what I'm misunderstanding. The taxable income is $22300. This is made up of $12300 ordinary ($40000 - $17700) and $10000 LT Cap Gains. You enter the ordinary tax table with $12300 which is all within the 10% bracket i.e. $1230 tax. The LT Cap Gains doesn't come into play because the taxable income of $22300 is within the 0% LT tax bracket.
