。
She embroidered her initials on a white handkerchief.
Literal
She [topic-は] white handkerchief [on-に] own's initials [object-を] embroidered.
Two katakana loanwords in one sentence: ハンカチ (from 'handkerchief,' English) and イニシャル (from 'initial,' English). The に on ハンカチ marks the surface on which the embroidery is placed — analogous to に for any 'do X on/onto a surface.' 自分の here is reflexive: her own initials.