Translation:His aunt is trying not to talk too much.
Although my answer: 'His aunt is trying to not talk to much' was actually a typing error, it is worth noting that in British English the rule of not splitting the infinitive, which only emerged in the 17th/18th century is not increasingly in abeyance.
I'm struggling to understand how to tell that my answer "His aunt is trying too hard not to talk" is wrong - although I certainly agree the given answer makes more sense!
In the answer given it is "not to talk to much" and yours is "trying too hard". The adverb is modifying something else.
Yours would be "Jeho teta se příliš snaží nemluvit.". You move the adverb before the word it modifies.
I'm wondering why "his aunt is trying too much not talk" (which empathize the effort) is not correct