Sunscreen applied to the face in the morning is broadly still present at lunchtime. The same application on the backs of the hands usually is not, and the reason is mechanical.
How a sunscreen film works
Sunscreen is a continuous film of filters suspended in a vehicle. Protection depends on that film covering the skin at an adequate and even thickness.
Filters absorb or scatter ultraviolet light where they sit. A gap in the film is not partially protected; it is unprotected at that spot.
Laboratory sun protection factor testing applies a specific quantity per area under controlled conditions, which is why real-world protection is usually lower than the number implies.
Why hands lose the film fastest
Handwashing is the dominant factor. Soap and water are designed to remove oils and films from the skin, and sunscreen is exactly that kind of film.
Hands also contact objects constantly, and every wipe on clothing, grip on a steering wheel or handling of paper transfers product off the surface.
Skin on the back of the hand flexes with every movement, which stresses a dried film in ways that flatter facial surfaces do not.
Why the exposure is high to begin with
Backs of hands face upward and outward during most daily activity, so they receive sun at angles closer to direct than most vertical body surfaces do.
Driving adds a significant load. Automotive side windows filter long-wave ultraviolet far less effectively than laminated windshields do, and the hands rest in that light.
The combination of high exposure and rapid removal is why the hands accumulate visible photodamage earlier than areas people think about protecting.
What ultraviolet light does to the tissue
Ultraviolet exposure degrades collagen and elastin in the dermis and disrupts the enzymes that repair them, so the supporting structure thins over years.
It also stimulates pigment-producing cells unevenly, which is the mechanism behind the flat brown patches that develop on chronically exposed skin.
These changes are cumulative and gradual, which is why they appear as a step change to someone who notices them suddenly in a photograph.
Where a physician belongs in this
Any spot on the hand that changes in size, color, border or texture, bleeds, or fails to heal should be evaluated by a dermatologist.
Hands and forearms are common sites for skin cancers precisely because of chronic exposure, and distinguishing a benign lesion from one that is not requires examination.
Reapplication after washing addresses the film problem. It does not address a lesion, and the two questions should not be treated as one.