Dorsiflexion of the hand is sometimes referred to as dorsiflexion of the wrist. Whichever description of the movement is used, the meaning is the same: flexing the wrist joint so that the backs of the fingers (that is the surfaces of the fingers that includes the finger nails) move backwards - towards the lower-arm to which the wrist and hand is attached.
Supination is a movement that can occur (in different ways) at the lower-arm and wrist and also the foot/ankle. The action of supination can be described for each case: supination of the forearm = rotation of the forearm turning the palm of the hand outwards so that it faces away from the body , i.e. turning the palm superiorly (= upwards) or anteriorly (= forwards).