Final answer:
Rahim Khan summoned Amir to Pakistan to seek his help and share important information about his family and their past.
Step-by-step explanation:
Rahim Khan summoned Amir to Pakistan because he needed his help with a personal matter. Rahim Khan was ill and wanted to share some important information with Amir regarding his family and their past. He wanted Amir to come to Pakistan to take care of an unfinished business and make amends for past mistakes.