What are the main challenges in Amir's quest in The Kite Runner? What is the significance?
Your question iss not very specific, but I assume that you are referring to Amir's trip to Pakistan to see Rahim Khan and his resulting return to Afghanistan. After learning the news from Rahim that Hassan and his wife have been killed, he discovers two important life-changing facts: Rahim tells him that Hassan is actually his half-brother, fathered by Baba; and that Hassan has a son, Sohrab--Amir's half-nephew--who is somewhere in Afghanistan. Rahim explains to Amir that "there is a way to be good again." If he can find Sohrab and return him to safety, it will allow Amir to ease his conscience about his betrayal of Hassan as a youth.
But it will not be an easy journey. He must travel into Taliban-held Afghanistan, no easy feat. He must hire a trustworthy guide and disguise himself, since the Taliban often beat or kill men with no beards. He must find Sohrab, since he is no longer at the orphanage he visits. Once he learns that Sohrab is being held by the Taliban, he must find a way to bribe them in order to obtain his release. If all of the above is accomplished, he must find a way to escape Afghanistan and then find a proper home (or obtain a visa) for Sohrab.