This is the 11239th most frequent Turkish word.
düğünü
"Wedding" (possessive form: "his/her/its wedding").
Here, 'düğünü' refers to a specific wedding, with 'Ayşe ve Mehmet'in' as the possessive context.
Ayşe ve Mehmet'in düğünü çok güzeldi.
Ayşe and Mehmet's wedding was very beautiful.
In this sentence, 'düğünü' indicates a particular wedding that 'they' had planned, showing possession.
Düğünü iptal etmek zorunda kaldılar.
They had to cancel their wedding.
The usage of 'düğünü' in this sentence implies a specific wedding that the speaker assumes the listener knows about.