Your LTCG is treated as the last income received when determining the tax bracket into which any particular income falls. Generally speaking, when determining your tax, the LTCG is subtracted from your taxable income, ordinary income tax is calculated on the remainder, then added to that is the tax on your LTCG calculated at LTCG rates. For 2017, the LTCG rate (0%, 15% or 20%) is determined by the tax bracket in which the LTCG would have been taxed if it had instead been ordinary income. For 2018 and later, the LTCG rates are determined by dollar thresholds (adjusted for inflation) rather than tax brackets where the income would have fallen as ordinary income, decoupling the LTCG brackets from the ordinary income tax brackets, but with similar effect.
In your example, your $96,000 of ordinary income is taxed the same amount as it would be if you had no LTCG. Add to that 15% tax on the $100,000 of LTGC. (This assumes that $96,000 is your taxable income without the LTCG. $96,000 is your AGI, you have sufficient deductions to bring you under the LTCG "maximum zero rate amount" of $77,200 (for 2018, adjusted for inflation in later years) and you are married filing jointly, some of your LTCG will be taxed at 0%. If are not filing jointly, the maximum zero rate amount is $38,600 and your ordinary taxable income is likely to be above that, pushing all of the LTCG in to the 15% LTCG bracket.)
