Learn Russian: Он многое видел в жизни.

Много is an adverb of quantity that usually requires a noun in the genitive case (like много людей for 'a lot of people'). Многое, on the other hand, is a neuter pronoun that acts as a standalone noun meaning 'many things' or 'a great deal'. Since 'a lot' is the direct object here and stands entirely on its own, многое is used.

How does многое fit into our current lesson on subject-verb agreement with quantifiers?

In this specific sentence, многое is the direct object, so the verb видел simply agrees with the masculine subject Он. However, if многое were the subject (e.g., 'A lot happened'), you must use a neuter singular verb: Многое случилось. Unlike collective nouns like большинство, the pronoun многое is strictly neuter singular and never triggers a plural verb.

The English translation says 'in his life', but there is no word for 'his' in the Russian sentence. Is it implied?

Yes. Russian naturally omits possessive pronouns like своей (his own) when the owner is already obvious from the subject of the sentence (Он). While you could grammatically say в своей жизни, leaving it out is much more natural and standard.

Could we use the standard Subject-Verb-Object order and say Он видел многое в жизни?