Final answer:
Black & Red Corp. must recognize a gain of $6,000 on its corporate tax return due to the distribution of a machine with a fair market value of $10,000 and a basis of $4,000 to its shareholder.
Step-by-step explanation:
Black & Red Corp. has to recognize a gain on the distribution of the machine to its shareholder, Mike. Since the company distributed machinery with a fair market value of $10,000 but its basis in the machine was only $4,000, the company recognizes a gain of $6,000, which is the difference between the fair market value and its adjusted basis.
In tax terms, this transaction is treated as if Black & Red sold the asset to the shareholder for $10,000, resulting in a gain that must be reported on Black & Red's corporate tax return.