The Walkie-Talkie Mystery — Carolyn Keene

Mystery mouth's voice is Nancy's first clue!
Nancy has a new set of hot green walkie-talkies to use in busy places like the mail. But when Bess and George try them out, one of the walkie-talkies disappears. Nancy thinks a bratty boy they know may have taken it.
Then Mystery Mouth starts sending Nancy messages on the remaining walkie-talkie. Each message contains a clue. Soon Nancy and her friends are on a crazy chase all over town. Mystery Mouth is talking, but it's Nancy who's doing the walking -- to find out who walked off with the walkie-talkie!