You are located in New York, NY, United States. Your friend is located in Panama City, Panama. You see a waning gibbous in your clear night sky. What phase, if any, will your friend see if the night sky in Panama City is also clear?

Waning gibbous.

Explanation:

The same side that you see in one place of the continent at night, you will also see in other place on earth, regardless of the hemisphere. There is however a slight difference, but not ecognizable to the human eye thus Waning Gibbous will also be seen everywhere else in the night sky that night.