My four year old daughter is terrified of our mostly docile six month old beagle puppy.?

If you just adopted the puppy yesterday then just be patient and give her time. Seeing as it's only a 6 month old puppy I'm uming he's really hyper and playful? That might scare her. Do as the first answerer suggested. Teach by example. She will eventually learn that the puppy will do no harm to her. The more she sees that the puppy won't hurt her, the more she will trust being around it. Good luck to you!