Cost refers to how much you originally paid for the item(s). For most items, you can't claim a deduction larger than what you paid for it in the first place.
Adjusted basis refers to an item whose original cost (to you) has been materially affected by certain transactions. See the list below for more information.
For your typical household item being donated (clothes, furniture, appliances, etc.) there will not be adjustments to basis, so just report the cost.
***From TurboTax Help***
Adjustments to basis (your original cost) include sales tax, freight, installation, excise taxes, commissions and recording fees charged for stock purchases, and legal fees that must be capitalized.
Increases to basis include costs you cannot deduct, such as:
- Improvements having a useful life of more than one year.
- Amounts spent after a casualty to restore damaged property less any insurance reimbursement.
- Rehabilitation expenses less any allowable rehabilitation credit.
- Legal fees to protect title and property.
- Assessments for local improvements (streets, sidewalks, etc.).
Decreases to basis include costs you can deduct, such as:
- The section 179 deduction.
- Deductions previously allowed (or allowable) for amortization.
- Depreciation and depletion.
- Gain from the sale of your home on which tax was postponed.
- Investment credit taken and casualty and theft losses (less any insurance reimbursement).
- Rebates received.
- Tax credits or refunds for buying a diesel-powered or electric vehicle, and the residential energy credit.
