。
She has lots of handkerchiefs.
Literal
She [topic-は] a-lot handkerchief [object-を] [has-持っている].
ハンカチ is a clipped loanword from English 'handkerchief' — and culturally significant: in Japan, the handkerchief is treated as essential daily-carry. Public restrooms typically lack paper towels or hand dryers, so people carry their own ハンカチ (often paired with a small ハンドタオル) for drying hands after washing. School-age children are routinely instructed to bring one daily. So 'she has lots of handkerchiefs' is less like 'lots of throwaway tissues' and more like 'lots of an important everyday accessory.' たくさん is adverbial here, modifying 持っている.