The fighter jet, the star of the image, is an F-16 Fighting Falcon deployed with an unspecified unit. When snapped on film, it was flying over New Mexico and met up with a KC-135 Stratotanker flying out of Fairchild Air Force Base in Washington.
The photo was taken during a training mission being conducted as a means for F-16 crews to maintain mission readiness. We are not being told what the mission was or for how long it lasted.
Generally, an F-16 can hold enough fuel (up to 7,000 pounds/3,175 kg internally, or 12,000 pounds/5,440 kg with two external fuel pods) to travel more than 2,000 miles (3,200 km), ferry range (far less when in combat configuration).
Depending on the mission profile and the pilot’s stamina, that can be prolonged, theoretically, to forever thanks to aerial refueling. Sadly, although there are countless F-16s flying in the service of a large number of national air forces, we have no data on the longest distance covered by such a plane in a single outing.