Why cant you get a tan on your palms?

Skin contains the pigment melanin which is activated by exposure to light. The palms of your hands and the soles of your feet have much thicker layers of skin due to their regular contact and friction with other objects (the ground, tools, etc). Melanocytes exist in the dermal layers of your palms and soles, but are buried beneath the more callous layers and are rarely directed at the sun. You could in theory try to tan your hands but the results would be pretty minimal compared to the rest of your body.