V/A+ 는데/은데/ㄴ데 V+ 어/아/여 줄 수 있어요?

It is used to introduce a situation in the preceding clause to ask about the content of the following clause by the listener. The following clause should include the expression asking about the possibility of the listener.

For an action verb, you should use ‘-는데/은데/ㄴ데’/ After the stem of ‘있다’, ‘없다’, you use ‘-는데’. After the stem of a descriptive verb that ends with a vowel or ‘ㄹ’, you should use ‘-ㄴ데’, with another consonant, you use ‘-은데’.

For ‘-을/ㄹ 수 있어요?’, if the stem of an action verb ends with a vowel or ‘ㄹ’, you use ‘-ㄹ 수 있어요?’, with another consonant you should use ‘-을 수 있어요?’.

컴퓨터 프로그래밍 과제가 있는데 좀 도와줄 수 있어?
I have a computer programming assignment. Can you help me?

사과가 너무 비싼데 값을 좀 깎아 주실 수 있어요?
The apples are too expensive. Can you give me a discount?

중요한 회의를 하는데 음악 소리를 좀 줄여 주실 수 있어요?
Can you turn down the music? We are having an important meeting.

Conversation:

민철아, 저기 있잖아…. 부탁이 좀 있는데….
Hey, well…. I’d like to ask you a favor…

무슨 부탁인데 그렇게 뜸을 들여.
What’s the flavor that makes you so hesitant?

너도 알다시피 우리 집이 회사에서 멀잖아. 그래서 회사 근처에 자취방을 얻었어.
As you know my house is far from the company. I got a room near it because of that.

잘했어. 출근 시간만 두 시간이 걸렸잖아.
Well done. It used to take you two hours to get to work.

그래서 이번 주말에 이사를 가는데 혹시 좀 도와줄 수 있어?
So I’m moving this weekend, could you please help me?

이번 주말? 아! 요즘 몸이 좀 안 좋아서 힘들겠는데.
This weekend? Oh! I’ve been feeling a little sick lately, so I’m afraid I can’t.

친구 좋다는 게 뭐냐? 짐도 박스로 세 개밖에 없어.
What are friends for? I even have only three boxes of luggage.

농담이야. 그 대신 점심은 맛있는 걸로 사 줄 거지?
Just kidding. You are going to buy me a delicious lunch for that, right?

Related words
뜸을 들이다 to hesitate
자취방 self-caring studio apartment, rented room
얻다 to get
프로그래밍(programming) Programming
(소리를) 줄이다 to reduce(volume)

Source: Yonsei University. Korean Language Institute