Final answer:
The taxpayer would realize a long-term capital gain by accepting the $10,000 offer to vacate the apartment since the lease, which is considered a capital asset with no tax basis, was held for more than one year.
Step-by-step explanation:
When analyzing the taxpayer's situation, we understand that the lease is a capital asset and typically, capital assets can generate capital gains or losses upon their disposal. Since the lease has no tax basis and the taxpayer would receive $10,000 for vacating the apartment, this amount represents a gain. The characterization of this gain depends on how long the taxpayer held the lease.
Considering the lease began 16 months ago and is held for more than a year but less than two years by the time of the offer, any gain from the cancellation of the lease would be classified as a long-term capital gain. A short-term capital gain is a gain on the sale or exchange of a capital asset held for one year or less, whereas long-term is for more than one year. Since the lease was held for 16 months, which is longer than one year, the correct answer is that the taxpayer would recognize a long-term capital gain upon accepting the landlord's offer to vacate.