GIVE ANSWERS - Türkçe

-dığını gives the meaning of 'he says THAT he lives in berlin' to the sentence, but in the other way -masını means that 'he says him or her TO live in berlin' i hope you'll understand

i'm not sure that i can make it clear like crystal but i'm gonna give it a shot anyway. suffix "dığını" might be refer to "that" in english.to examplify, "he says that he lives in berlin"(berlin'de yaşadığını söylüyor).suffix -masını can be traslated as "he says live in berlin".in the second sentece you wrote there are two people .first, the one says someone that you should live in berlin. second, the one that is adviced to move berlin. i hope it helps i tried to do my best i know it's a little bit rough explanation

Berlinde yaşadığını söylüyor" ( He/She says lives in Belin )
The orther one, "Berlinde yaşamasını söylüyor" ( Him/Her says, him/her to live in Berlin )

"Berlin'de yaşadığını söylüyor" this sentence means "He says he lives in Berlin."
"Berlin'de yaşamasını söylüyor." means "He says he have to lives in Berlin"