Final answer:
The Federal Communications Commission (FCC) is the government organization that approves a cable operator's adding and/or deleting of services.
Step-by-step explanation:
The government organization that must approve a cable operator's adding and/or deleting of services is the Federal Communications Commission (FCC). The FCC licenses cable television systems, regulates cable pricing, technical standards, and programming. They also require that certain local broadcast programming be made available through cable systems and that at least one noncommercial channel be carried on every cable system. Additionally, the agency mandates that cable systems have a formal equal employment opportunity program, monitors compliance, and investigates claims of discrimination.