For which of the following circumstances would a taxpayer likely file a form W-4?

A taxpayer would file a form W-4 primarily to establish withholding allowances for income tax. The W-4 form is crucial for employees to communicate to their employer how much federal income tax should be withheld from their paycheck. By filling out this form, taxpayers can adjust their withholding based on their personal and financial circumstances, including marital status, number of dependents, and whether they have other sources of income. This helps them avoid owing a large tax bill at the end of the year or having too much withheld throughout the year, which can result in unnecessary loss of income.

The other options, while relevant to tax situations, do not pertain directly to the purpose of filing a W-4. Determining the tax deductibility of a mortgage involves different forms and financial documentation and is tied to personal tax returns rather than withholding adjustments. Claiming a refund for excess withholding is typically done at the end of the tax year on a tax return, not through a W-4. Establishing eligibility for Social Security involves different processes and documentation, separate from income tax withholding issues. Thus, option B accurately identifies the purpose of the W-4 form within the context of payroll and tax withholding.