Final answer:
The taxpayer does not need to clear the Capital gain limitations to deduct an operating loss from a flow-through entity.
Step-by-step explanation:
From the given options, the hurdle that the taxpayer does not need to clear to be eligible to deduct an operating loss from a flow-through entity is the Capital gain limitations.
1) Material participation requirement: This hurdle requires the taxpayer to actively participate in the business to claim deductions.
2) At-risk rules: This hurdle limits the amount of deduction a taxpayer can claim to the amount they have at risk in the business.
3) Passive activity loss limitations: This hurdle restricts the deduction of passive activity losses to the extent of passive income.
Therefore, the correct answer is 4) Capital gain limitations.