。
My older sister has three times as many books as I do.
Literal
My older-sister [topic-は] my three-times books [object-を] holds.
三倍 attaches to 私の to mean 'three times mine,' and the noun being multiplied (本) follows directly without an extra particle — Japanese can collapse 'three times the number of books I have' into the compact 私の三倍本. This implicit/elliptical pattern works fine in casual contexts where the reference is clear; a more explicit phrasing would name the counter (三倍の冊数の本) for unambiguous formal writing. 持っている for 'to have' is the standard possession verb, in resultative ~ている because possession is a held state, not a momentary action.