"Finally we hear news that we are pleased with."
Translation:Sonunda sevindiğimiz bir haber duyuyoruz.
Just a general observation: In multiple-choice translations I have noticed that there is almost always a wrong choice with a word of Arabic origin, which I assumes to be an outdated word from Ottoman Turkish. Actually now whenever I see a sentence with an Arabic word in a mutiple-choice exercise, I instinctively dismiss it as incorrect :/
First of all there is no word as beğlenmek. You must mean beğenmek. "Sonunda hoşumuza giden bir haber duyuyoruz" can be used here but we don't say beğendiğimiz bir haber. Because beğenmek is something like to think and decide, to choose. There is a thinking process and liking and choosing meaning. "sağda oturan kızı beğendim", "kırmızı elbiseyi çok beğendim".
Both the English sentence construction and Turkish translation sound contrived and unusual.
"Finally, we hear good news" "Sonunda, sevidirici (bir) haber/iyi (bir) haber" duyuyoruz ", seems a better Turkish translation than "sevindiğimiz haber" which sounds quite unnatural to me.