It's always tricky with these things. For sure this way of asking questions is widely used in spoken language. So it's not a matter of correctness, it's a matter of how spoken/slang we want to go :)
I'm not even sure my self what my opinion on this is x) Technically, accepting "You read this?" makes "You read this." automatically accepted (Duo is not sensitive to punctuation). But, well, in Ukrainian, the difference between a statement and a question is only the question mark anyway, so...
The alternative suggestion - 'You read this?' - is an example in English of asking the same question by intonation, rather than by changing the word order; so it should be accepted as a variant by Duolingo. In fact, I think it is a better translation of the question Ви читали це?, since it is a one-to-one mapping with the Ukrainian words and it better shows the structure of this form of question, which seems a more common form in Ukrainian, i.e. the use of intonation to ask a question (or the question mark in the written form). Also, it is worth noting that the word 'read' in this question is pronounced |red|, since it is in the past tense, and not |reed|, which is the present tense. This is another example in English of the pronunciation changing, but not the spelling (just to confuse children and non-English speakers!).
Update from now, a year after: this version is accepted in many (I would like to say most... but maybe not) sentences here :) If you see it missing, simply report.
Yes and no :)
Ukrainian has only one form of past tense - no perfect and no continuous. So, no difference there. However, aside from the tense we have the so-called "aspect" of the verb which can give information about whether the action was totally finished or not. So some difference :)
Basically, Ви читали це? is asking about the fact of reading - no matter whether you read the book/magazine/sentence/etc. till the end or not.
Ви прочитали це? is asking whether you finished the book/magazine/sentence/etc., read it till the end.
So, Ви читали це? can be translated as "Did you read it?", "Have you read it?" or "Were you reading it?"
Ви прочитали це? can be "Did you read it?", "Have you read it?", "Have you finished reading it?", "Did you finish reading it?" etc.
The grammar is not really one-to-one so it's tough to translate sometimes :)