Thank you for the question. So the vaunted, and rarely seen, $0 result. I have only seen it once on an assisted phone call in four years, and the customer could not understand how. Eventually after a half hour they understood.
It is highly unlikely that you would get a zero dollar result. Just fill in the W-4 using these two resources and hope that it is $0.
See both:
TurboTax's W-4 Calculator
TurboTax's Tax Caster tax calculator
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