This is the 7480th most frequent Turkish word.
gücenmez
"Not offended" or "does not take offense."
Here, 'gücenmez' is used as a verb in the negative form meaning 'does not take offense'.
Ali, kendisine yapılan eleştirilerden pek gücenmez.
Ali doesn't easily take offense at the criticisms made about him.
In this case, 'gücenmez' emphasizes a personality trait of being forgiving or emotionally resilient.
Olaylara karşı oldukça sabırlıdır; bu yüzden kolay kolay gücenmez.
He is quite patient with events; therefore, he doesn't get offended easily.
The usage here indicates a trust and a forgiving nature towards friends.