I'm not English native speaker, but as far as I know, you don't need the auxiliary "do" (the first "do" you wrote) for indirect questions, as in this case.
In direct questions, you need that auxiliary. An example of direct question is "Come lo fanno?" ("How do they do it?"). In this case, the auxiliary is necessary.
If "chiedete" = "you ask" in the hint, then why was it not acceptable in my answer "You ask how they do it!"