When to use litteris Latinis
I must admit that I am confused. When should I use litteris Latinis and wherein should I use litteras latinas? I know that the people at Duolingo are making it easier for me but I would love to hear about easy way to separate the above terms.
You need to understand the difference between different parts of speech and the "cases" that each word needs to have when it's a different part of the sentence.
I wrote a long post about this - sorry I don't have the link to it, but you should be able to find it somewhere in the Latin forum.
This isn't just for Latin that it's important, nor is it unique to Latin. Understanding parts of speech is an important part of English grammar too, but sadly not enough is taught about it in schools these days, and, of course, English word endings don't change very much like Latin ones and those of many other languages.
The short summary is that "litteris Latinis" is dative case (plural) which can often be found with the verb studere which would require that case. It could be in the ablative case, which has the same ending for a word in this declension, if there was some reason in the rest of the sentence to make it ablative.
Litteras Latinas is accusative case and would normally be used when it's the object of the sentence.
But it's not quite that simple...
EDIT: (Post corrected after scrambled brain mistake pointed out and noted - sorry if it caused confusion)
As someone else pointed out, "litteris Latinis" is either dative or ablative.
The issue with this phrase on Duolingo arises with the verb "studere", which normally takes a dative instead of the accusative (unlike what anyone would logically guess at first). Duolingo, for some strange reason, throws this into the first lesson that focuses heavily on accusatives, which throws a lot of people off (myself included, the first time around).
The TLDR for completely new people is: (a) As the subject of a sentence (like "Latin is her native language") you want the nominative case "litterae Latinae". (b) With most verbs (like "legere" -- "to read") you want the accusative case, "litteras Latinas". (c) But specifically with the verb "studere", you want the form "litteris Latinis".
I agree that "studere" is not the best choice of verb to use in examples for beginners (as is the case for a couple of deponent verbs appearing here and there, imho). This is all the more true with this verb for we are biased by today's meaning of the word "study". It might help to know the original meaning of the word "studere" https://latin-dictionary.net/search/latin/studere which somehow explains why the dative is used instead of the accusative.
The sentences so far show two options for "Latin literature," with two different verbs that require different 'cases' of the phrase, Latin literature.
If you're learning Latin literature (verb discere ), you need to use the accusative-case form of the phrase: Litteras Latinas discunt (They are learning Latin literature). The verb discere is a transitive verb ( = needs a direct object).
If you're using the verb studere , you need the dative case (litteris Latinis ), simply because the verb is not transitive and is one that requires dative.
There are a few verbs that require to be constructed with the ablative case: Litteris Latinis utuntur , "they use / employ Latin literature."
Nothing beats checking a dictionary and seeing if the verb is transitive ( = takes a direct object in the accusative case), or requires a dative (or even ablative).