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She puts a lot of time into practicing the piano.
Literal
She [topic-は] piano [of-の] practice [to-に] much-of time [object-を] applies.
時間をかける ('to spend time on') is one of the productive ~をかける idioms, where かける ('to apply, hang, pour') turns a noun into a verb of dedicating: 手間をかける ('take pains'), お金をかける ('spend money on'), 心を掛ける ('pay attention to'). 多くの ('much of, many of') is the noun-modifying form of 多い ('many, much'), used before nouns where 多い alone would be ungrammatical (you say 多い人 only in some contexts; for general 'many people' the word for 'many of...' is 多くの人). The に here marks the destination of the time being applied — the practice is what receives the time.