。
She wiped her face with the handkerchief.
Literal
She [topic-は] handkerchief [with-で] face [object-を] wiped.
ふく (拭く) means to wipe or rub clean — sweat, water, dust, smudges. で marks the handkerchief as the instrument; 顔を marks the face as the surface being wiped. Japan's hot, humid summers make handkerchiefs essential carry items for wiping sweat from face and neck — the daily-carry habit is reinforced by the climate as much as by the absence of paper towels in public restrooms.