From 2018, long-term capital Gains (LTCG) are taxed at 0%, 15% or 20% depending on your tax brackets.
For the purpose of determining your LTCG tax rate, LTCG are added to your ordinary income.
Your tax bracket for your ordinary income depends only on your ordinary income. Your LTCG will not push you to a higher bracket.
In your example above, if you are married filing jointly, at $96,000 of taxable ordinary income, your tax bracket will be 22%.
If you had $100,000 of LTCG, it will bring your total taxable income to $196,000 to determine your LTCG tax rate which will be 15%. But your ordinary income tax bracket will still be 22%, and not pushed up to 24%.
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