"The teacher reads Latin literature."
Translation:Magister litteras Latinas legit.
"Litterīs latinīs" would be either dative or ablative, and would be suitable for "Magister litterīs Latinīs studet", because "studeo, -ēre" (to apply oneself to) takes the dative.
"Lego, -ere" (read) is a normal transitive verb, so it takes the accusative, "Magister litterās Latinās legit".
"Litteras Latinas" is in the accusative case because it is the direct object of "legit". What is being read?
"Litteris Latinis" is in the dative case and is declined that way for "Magister litteris Latinis studet", because "studere" means "to dedicate oneself to" and therefore does not take the accusative case but rather the dative.
Here is a plain-English overview of what the cases are and how they work:
Latin cases, in English
Adjectives must agree in gender, number, and case with the nouns they modify, but they have their own declensions. Sometimes you get lucky and the adjective just happens to follow the same declension as the noun, but that is not a guarantee.
I've just been counted as correct for 'litteris latinis legit', which Duo counted merely as having typos, but it's frankly an error in the inflection of both adjective and noun. On the other hand, I've been marked wrong in some sentences when the only 'error' was to misspell Corinna. Seems to me that for learning Latin, any 'typo' in the inflection should be counted as a mistake, while a mistake in the spelling of names should get by as typos. But I am grateful that they've got this course started, and realise that it is just Beta at this point.