"Imitate this sound."
Translation:E hoʻopili mai i kēia kani.
Have to agree with DL on this one because of the word "kēia." That would indicate the speaker is making (or producing) the sound, and thus use of "mai" is appropriate (imitate me). If you wanted to use "aku" because you're asking someone to imitate the sound that a teacher is making, you would have to use "kēlā kani" instead of "kēia kani": E hoʻopili aku i kēlā kani. You could probably think of some situations that are pretty weird, but those are the two most obvious situations for this sentence.
This is from my own experience as a Hawaiian speaker (having not studied it in a classroom), but "mai" is directed towards the speaker and "Aku" is directed away from the speaker. So if you are saying "e ho'opili mai," the implication is that you (the speaker) want the listener to copy something you are doing. "e ho'opili Aku" implies that you want the listener to imitate someone else. Like if I told a child to imitate the teacher who is not me- e ho'opili Aku I ke kumu." If you're not including someone else in this directive, then the assumption (I think) is that the person is expected to imitate something you (as the speaker) are doing.
Again, that's my non-academic take on it as someone who speaks Hawaiian but did not learn it in an academic setting (so there may be a different distinction).
That was the logic i was using when I used "E ho'opili aku" - since there was no implication that the sound to be imitated was something the speaker was making. It could just as easily have been a request to imitate the song of the shama outside the window. I guess I'm still not clear on how to infer the implication of the speaker correctly.