Is it possible to wear a patch on the palm of my hand or on the sole of my foot?

For a start, these would not be very practical places to wear them. The patch is less likely to stay attached to these areas because of the way the skin bends when you use them. It is not advisable to wear a patch on your hand because you increase the chance that you will accidentally transfer residue nicotine to your eyes or nose. This why you should always wash your hands after removing or applying the patches. More importantly, the skin of the hands and feet are less suitable for the transferral of the nicotine in the patches.