I recommend you are seen by a reputable clinic or skincare proffessional to rule out any skin disorders, but this sounds to me like pigmentation. This can be treated with IPL intense pulsed light to even the skintone - supplement this with lightening skincare such as my SkinScription Medilight Serum with lactic acid and liquorice root to lighten and brighten dark patches.
If you are suffering with poor circulation this could be a cause for lighter pale hands. Generally there will be a natural difference in pigmentation as your face is more likely to be exposed to sunlight. If the difference is marked, and you also feel cold in the hands, with restriction of movement in cold weather, this could indicate a condition called Raynauds. Of course it is difficult to narrow down an exact cause without knowing more about your constitution and medical background. It is advised to consult a dermatologist should there be any related medical concerns. Treatment-wise, acupuncture is very good at improving circulation. Massage and detox using Ayurvedic herbs are wonderful for improving circulation and complexion of the skin (whether that be of face or peripheral areas).
Sounds as though the face has gotten more sun exposure than the hands.Or, the hands have been cover with gloves or something, while the face has remained exposed, thus causing a darker pigmentation on the face? Or, is there some hormonal changes or medications that you might be taking that is resulting in a darker pigmentation on the face? New product usuage on the face area? I would also be interested in knowing whether your neck and decollette' areas are effected, as well? If you are worried, I would suggest that you visit your dermatologist to get an exact diagnosis. I would not try to darken the hands to match the face or vice versa. Find out exactly what the problem is. Lets hope that it is not something similiar to vitiligo.