My boyfriend is getting dry skin patches that are very red on his hand. What could this be from?

Eczema. There are a few considerations, but eczema would be one that is fairly common. Dry skin itself is also common and can sometimes cause dry patches. Try using a non-perfumed cream or ointment right after showering while the skin is still damp, as well as 2-3 other times a day. If still a problem he should see his doctor.