This is a toothbrush holder. It is meant to be used with 3M "Command" double-sided adhesive strips, which near as I can tell are black magic. Just stick it on the wall with the long part pointed up (to minimize the peel leverage) and it'll stay there for years even if you brush twice a day (and you should!).

Print it in different colors for each kid so they know that theirs is the {blue|red|pink|sparkle|glowinthedark} one.