Sentence Analysis

I have to analyse the following sentence, but I'm really stuck...

"Amanda's practical solutions of what had seemed an insoluble mystery descended on the family like a balm."

I have to cut this sentence into constituents and cut those up in nouns, verbs, adverbs, adjectives, pronouns, prepositions etc.
For now I have this:
'Amanda's practical solutions of what had seemed an insoluble mystery' = the subject of the whole sentence and is a Noun Phrase
'descended' = the main verb of the sentence,
'on the family' = a Prepositional Phrase
'like a balm' = a Prepositional Phrase

The two prepositional phrases don't give me any trouble (both start with a preposition, than have a determiner article and end in a noun).

The Noun Phrase is what gives me trouble...

'Amanda's practical solutions of what had seemed an insoluble mystery' has two constituents, I'd say...
'Amanda's practical solutions' = Noun Phrase
'of what had seemed an insoluble mystery' = ???
I really can't get beyond this point... How should I analyse this?

I really hope someone can help me with this sentence...