、。
I offered to help her with her homework.
Literal
I [topic-は], her [of-の] homework [of-の] help [object-を] offered.
申し出る ('to offer, to propose') is the verb form of 申し出; here the noun form 申し出 appears as the object of する as an alternative: 申し出をする. Stack of possessive の links 'her + homework + help.' 'Offer [of] help [with] homework' — Japanese chains these all with の.