V. + (어/아)도 돼요? => "Is it all right if/to . . . ?," "Is it okay if/to . . . ?"

V. + (어/아)도 돼요?

=> "Is it all right if/to . . . ?," "Is it okay if/to . . . ?"

This construction asks for permission in an informal and casual way. 

• 한국말로 물어도 돼요?
  => May I ask you in Korean?
  네, 물어 보세요.
  => Yes, go ahead.
  
• 지금 집에 가도 돼요?
  => May I go home now?
  가도 돼요.
  => Yes, you may.
  아니오, 가면 안 돼요.
  => No, you may not.
  
• 숙제를 내일까지 내도 돼요?
  => Is it okay to turn in my homework tomorrow?
  네, 괜찮아요./네, 좋아요.
  => Yes, it's okay.
  
• 보고서를 연필로 써도 돼요?
  => May I write my report with a pencil?
  연필로 쓰면 안 돼요.
  => You may not write with a pencil.
  펜으로 써야 돼요.
  => You have to write in ink.
  

Notice the differences in the positive and negative answers:

• -(어/아)도 돼요?
  => "Is it all right to . . . ?"
  
• 네, . . . -(어/아)도 돼요.
  => "Yes, it's all right . . ."
  
• 네, -(어/아)도 괜찮아요/좋아요.
  => "Yes, it is fine."
  
• 아니오, . . . -(으)면 안 돼요.
  => "No, (one) must not . . . ," "it should not . . . ,"