'소원으로 고백을 받아 달라던가?'
== 소원으로(as a wish) 고백(a confession)을 받아(receive, accept) 달라던가?(did they ask for it?)
== As a (formal) wish, he/she might have requested that his/her confession be heard?
== I am not sure, but he/she might have been asking me to hear their confession.
It's a a bit of a difficult sentence, with ~으로 and ~달라던가?. 고백을 받다 is also a little unclear in meaning.
* ~으로 = 1) to, toward, 2) by (a means), 3) as; as a token/symbol/justification.
* ~던가? = question ending form asking oneself about something one knew or experienced in the past.
달라던가? is the trickiest part.
- 달다 = ask for something. It is always used in the conjugation form 달라(는/고/며/면서/던/던가/etc).
- 달라고 (말)하다 = ask someone to give/hand something to the speaker.
- 달라다 = Shortening of 달라고 하다. Conjugates to 달라는, 달라고, 달라면, 달라던가, etc.
- 달라던가 = 달라다(달라고 하다) + 던가? = (I wonder,) did they ask for it?.
- V + ~아/어 달라다 = ask (someone) to do V for the speaker. 달라다 here is a helper verb expressing "do for someone".
- N을 받아 달라던가? = Did they ask me to hear/accept N (for them)?
If 받아 달라던가 is still unclear, you should practice phrases of the form 동생이 책(을) 달래 and 동생이 숙제를 도와 달래 (달래 = 달라고 해).