Final answer:
The rule that requires cable operators to black out a network show from a distant station if the local affiliate plans to broadcast the same program is called Syndicated exclusivity rules.
Step-by-step explanation:
The rule that requires cable operators to black out a network show from a distant station if the local affiliate plans to broadcast the same program is called the Syndicated exclusivity rules. Syndicated exclusivity rules ensure that the local affiliate has the exclusive right to air certain programs within their designated market area. This rule helps protect the local affiliate's investment in securing the broadcasting rights for the program and prevents competition from the distant station.