"They live with their grandfather."
Translation:वे अपने नाना के साथ रहते हैं।
साथ means "together". It also means the noun "side." So you can think of के साथ as "[by] X's side", i.e. "[together] with X". Also, it appears that के is invariable here, i.e. you would never (I think) see का साथ in the sense of "with" (but you could if "side" is meant). This is according to my research; I am not a native or fluent.