"My son's wife does not have a car, but she has a bicycle."
Translation:Benim oğlumun karısının bir arabası yok, ama bir bisikleti var.
I'll try to give you the idea. Both arabası and bisikleti are with the possessive suffix. For example, "he has a car" would be "onun bir arabası var", using genitive case in the pronoun O and possessive suffix for the owned thing Araba. You can get detailed information in Tips and Notes of Possessive lesson.
Karısının is karı + (s)ı + (n)ın. Karı is wife, karısı is wife in possessive form (she is my son's wife), and karısının is karısı in genitive case, meaning she's someone's wife that possesses something (owns "araba", that turns into "arabası" for being possessed).
To sum up, the wife first get the possessive suffix for being my son's wife, then she gets genitive suffix because she owns a car, with the buffer letters in between.
In « my son's wife does not have a car »= « the car of my son's wife does not exist » we have three groups of words : subject (my son's wife), object (car) and verb (does not have».
1- « The car » « the car » = « araba » : the possessed object of « my son's wife », at the possessive case > « araba-sı »
2- « Of my son's wife » « My son's wife » = « the wife of my son ». « Oğul» is the possessed object (of « benim ») , at the possessive case > «oğl -um » and the possessor of « the wife », so at the genitive case > « oğl-um-un ».
« The wife » = « karı » is possessed object (of the son), at the possessive case > « karı -sı » and the possessor of the car at the genitive case > « karı-sı-n-ın »
3- « Does not exist » = « yok