Can I zero out my capital gain distribution if my income is less than 80,000 (jpint)

No you can't zero it out. The capital gains are added to your other income to determine the capital gains tax rate. For a married filing jointly tax return, the total of up to $80,800 of your ordinary income plus capital gains less your standard or itemized deductions determine the tax rate on the capital gains. It is 0% for the amount of gains when added to your ordinary income that brings the total up to $80,800. Any amount above $80,800 up to $501,600 for married filing jointly is taxed at 15%.

How do you mean zero it out? Your capital gain distribution is included on your return. Capital Gains Distributions reported on Form 1099-DIV, Box 2A should be reported on Schedule D, Line 13.  On Schedule D, your Capital Gains Distributions are combined with any Short-Term or Long-Term Capital Gains or losses and this figure flows to Line 7 of your Form 1040.

Long-term capital gains tax is a tax on profits from the sale of an asset held for more than a year. The long-term capital gains tax rate is 0%, 15% or 20% depending on your taxable income and filing status.

LTCG Rates