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She has three times as many dictionaries as you do.
Literal
She [topic-は] your 3-times [genitive-の] book-count [genitive-の] dictionaries [object-を] holds.
Japanese can also express 'three times as many' more compactly with patterns like 君の3倍 + bare noun (collapsing 'three times your-count's worth' into a single phrase). The verbose phrasing here, by inserting 冊数 ('number of bound volumes') and chaining particles の~の~の, makes the comparison unambiguous: how many dictionaries each owns — not their total weight, value, or anything else. 冊 is the counter for bound volumes (books, magazines, dictionaries), and 冊数 nominalizes that into 'volume-count.' This kind of explicit phrasing is the formal/written counterpart to elliptical casual versions.