The amount of taxes is obtained identifying the correct interval in the table and then applying the proportions.
For a taxable income of $400,000, the tax is of $45,210 plus 35% of the income over $204,100, hence:
45210 + 0.35(400000 - 204100) = $113,775.
For a taxable income of $10,954, the tax is a simple 10%, hence:
0.1 x 10954 = $1,095.4.
For a taxable income of $108,962, the tax is of 12962 plus 24% over 84,200, hence:
12962 + 0.24 x (108962 - 84200) = $18,904.88.
For a taxable income of $209,850, the tax is of $45,210 plus 35% of the income over $204,100, hence:
45210 + 0.35(209850 - 204100) = $47,222.5.
Recapping, we identify between which two values the taxable income is located, and then apply the tax rule defined by the table for the range in which the income is located.