조용히 해 : Be quiet. 조용해 : It is quite. (or silent)

조용하다, adjective, to be silent/calm 조용해!, It is silent/calm!. This word is a conjugated form of 조용하다 in the speech level 해라체. Therfore, the followong conjugated forms can be seen. 조용해요 (in the speech level 해요체) 조용합니다 (in the speech level 하십시오체) 조용히 해, 조용히 해요, 조용히 하세요 (You should) Be quiet! Or Do it quietly! This is an imperative sentence. And the adverb 조용히(in a quiet/silent way) is used.

both are understandable. if you say 조용히 해 faster, it sounds like 조용해.