I bought something any kid his age will enjoy. = I bought something that / which any kid of his age will enjoy.
【分析】原句中有两处省略:
(1) that / which any kid his age will enjoy 是定语从句,something 是定语从句所修饰是先行词,that / which 是关系代词,在从句中作 enjoy 的宾语,所以可以省略。
(2) "of ... age"作后置定语时,介词 of 可以省略。例如:
She married a man (of) her father's age. 她同一个和她父亲年龄相同的男子结了婚。(摘自陆谷孙主编:《英汉大词典》第2版p.35)