A ship that has been on duty outside the limits of the United States continuously for a period of nine months or more may fly which pennant?

The homeward bound pennant is specifically designated for ships that have been deployed overseas for an extended period, typically nine months or more. This pennant serves to signify that the ship is returning to its home port after fulfilling its duties away from the United States. It communicates the ship's status and readiness to return home, allowing other vessels and ports to recognize that the ship has completed its assignment and is on its way back.

The other options, while they may seem relevant, do not accurately reflect the recognition given to ships based on their length of service abroad. The foreign waters pennant relates to operations in international waters but does not indicate a return. The long deployment pennant is not an official designation recognized in naval traditions. The admiral’s pennant signifies the presence of a flag officer but does not pertain to deployment duration. Thus, the homeward bound pennant is the correct and appropriate choice in this context.