One tool translates "Raise your hand high" as 高举你的手, which seems logical (high raise your hand). But another source says it is 高高的举起手. Why is 高 repeated, and what is the purpose of 的 in this sentence?
(Not from a gramattical standpoint).
高举你的手 is more imperative but it sounds really weird (nobody says this, perople will say something like 把手举高).
高高地举起手 sounds more polite and feel like it's someone talking to kindergardeners. Repeating the character puts more emphasis on the adjective high. The 的 is just to connect the adjective and he action, for instance, you could also say 快乐地举起手, raising their hands happily.
Something like 高地举起手would not be correct though