Why does my 4 nth old baby keep eating her fingers?

Four months is about the age when babies discover their hands -- and find that they're wonderfully useful! They most love using them to get anything they can into their mouths, including their fingers. Sucking can be a sign of hunger, but if your daughter is eating and growing well, I don't think she's hungry constantly. Most likely, she's doing it to soothe herself, which is a very normal behavior; up to a third of infants suck a pacifier or their fingers. Unless you're ready to substitute something equally relaxing as often as your daughter sucks her fingers, stopping her could be hard and pretty upsetting for everyone.