Translation:She usually reads two books each month.
"po" is explained on this site.
"po du" means "rate of two" and "monate" means "monthly"
Also, if this site can be believed, it should be "librojn" and not "libroj"
But "po" is only for the number, and not for the noun. Therefore the noun takes the case which it would take if "po" was not even there, as is explained in the link I sent
Now I found it and can quote: "Remember that po always takes as its object a numeral; any associated noun takes whatever it would have if the po weren't there at all."
So "po du" and "legas librojn".
I had to read up on it again, because I was very sure that there should not be an -n after po. Zamenhof himself mostly left out the accusative, but sometimes used the accusative after it. Standard Esperanto has no -n after po, but apparently due to a few mistakes(?) on LLZ's side, it seems to be optional. Here's the source (search for po or n-finaĵo): http://bertilow.com/pmeg/gramatiko/nombroj/nuanciloj.html
In any case, the Duolingo sentence above is correct.
Your way of analysis is but one possible. Why do you think po takes a number as its object? I don't think that's the case, usually. Mostly, po takes a number AND a noun as its object. To me, moving po tri to the front of the sentence is akin to saying something like: "Tri mi aĉetis pomojn." - that sounds awkward to me, if not wrong. Or: "Multajn mi aĉetis pomojn." - slightly less strange, but I wouldn't be sure if this is correct Esperanto, although I'd accept "Pomojn mi aĉetis multajn/tri."
To me, po is the head of tri pomoj(n) and thus can be regarded as a preposition, which would then not require an accusative according to classical Esperanto grammar. I think speakers tend to use the accusative there, now, and because Zamenhof used po sometimes with, sometimes without accusative, both should be accepted. Both are well-formed in Esperanto, although the accusative one is more common nowadays (I think; I didn't do a corpus analysis).
Ok. It seems that this has been changed at some point and I am of the newer system and you are of the older. We are both almost correct. Do not attack free word order, though. Remember that esperanto is an international language. The whole point of having an accusative is to free word order. Word order S-V-O used in ENG/GER/SPA is not a universal one. In many languages it is perfectly normal to say "Multajn mi acxetis pomojn" or "Pomojn mi multajn acxetis". You cannot say those are wrong just because of your preferences. Esperanto does not have the "ban everything" - attitude that english has.