They do sound the same BUT eventhough they have quite similar meanings, they have their own usage. "어떻게" purely means "How". You ask how you should do something or not. There are instances to that it is used as "What" Examples: 그걸 어떻게 알았어요? (How did you know that?) 이 계획을 어떻게 생각하세요? (What do you think of this plan?) 그동안 어떻게 지냈어요? (How have you been?) "어떡해" is a contraction of "어떻게 하다" which only means "What should I do?" or "What am I supposed to do?"

hi timmy 어떻게 = O (Correct notation) 어떡해 = X (Wrong notation) 어떡해 is Phonetically said

'어떡해'는 '어떡하다'에서 파생된 말입니다. '어떡하다'는 '어떻게 하다'의 준말입니다. 어떻게, how 어떡해, what should (I) do.