I was doing my reviews and got this sentence:
そんなに彼が好きだったら、__________ [つきあう]？
The correct answer was: 付き合ったらどう.
I answered: つきあってくれないか.
I feel like I must be missing some nuance? To me it seems てくれないか is more asking for a favor to a request (you wouldn’t ask someone out as a favor) where たらどう is more casual like “wouldn’t it be cool if we dated?”.
haha just kidding…
unless…?
You have てくれない right–that’s when you ask a favor for yourself (or in-group). たらどう is used when making a suggestion. In the sentence here, the speaker isn’t suggesting the listener date the speaker. The speaker is suggesting the listener should date “him” if the listener likes him (whoever that is).
Ahh Ok. I was thinking they were directly asking the listener, but you are saying instead it’s more of a general statement and the listener may not be the one being asked out. Makes more sense, thanks! 
Also be careful because たらどうexpressions can come off as condescending. As if the action is very obvious and you are not taking the transparently good option.
運動したらどうですか？- Hypothetically translates to, “what if you worked out?” but comes across more like, “You know it would be better if you worked out.”
So そんなに彼が好きだったら、付き合ったらどう. Is way more like, “You know, if you like him so much you really should ask him out. 
”
Right, I forgot to point that out. While たらどう is used to make suggestions, it’s also used to criticize indirectly. Context and tone will usually sort things out, but more words after たら are a good indicator. たらどう is only one word removed from the quite impatient sentence-ending particle たら・ったら, but if you add どうですか, it steers things away from that.
Yeah, I think so, too. I sense a tinge of impatience or frustration in this example sentence. I can easily see it in a long, protracted conversation between two girls where one is going on and on about the boy she likes and whether he will “notice her.” The other finally gets exasperated and says, そんなに彼が好きだったら、付き合ったらどう？