Can someone please help me understand this sentence?

The hint that I learned about cleaning the wall saved me much work.


The hint that I learned about cleaning the wall = noun phrase

that I learned about cleaning the wall = adjectival clause giving more information about the noun work.
that = object of verb learned?
I= subject of adjectival clause
learned = transitive verb

about cleaning the wall= prepositional phrase functioning as adjective or adverb????
about= preposition
cleaning = gerund = object of the preposition about
the wall = object of gerund


saved = main verb = past simple tense
me= indirect object
much= adjective modifying noun work
work= noun = direct object