Final answer:
Colby's recognized gain from the like-kind exchange is limited to the amount of cash, or boot, he received. Therefore, despite the realized gain being $46,000, he will only recognize a gain of $20,000, which corresponds with the cash received in the transaction.
Step-by-step explanation:
The question pertains to the recognition of gain or loss on a like-kind exchange involving real property used for business purposes. When Destiny exchanges her lot with an adjusted basis of $40,000 and additional cash of $20,000 for Colby's lot, valued at $36,000 (with a basis of $10,000), Colby realizes a gain. The gain calculated is the difference between the fair market value of what he received ($56,000 which is $36,000 plus $20,000 cash) and the adjusted basis of his original asset ($10,000), resulting in a realized gain of $46,000.
However, since a like-kind exchange is generally not fully taxable and he received cash (referred to as 'boot'), the recognized gain is limited to the amount of boot received. Therefore, Colby will recognize a gain of $20,000, which is the lesser of the realized gain and the boot received. This aligns with option A: $20,000 gain recognized due to Colby's receipt of boot.