。
She marked her umbrella with a red ribbon.
Literal
She [topic-は] her own umbrella [on-に] red ribbon [with-で] mark [object-を] attached.
Two particles share close real estate: に marks the umbrella as the location where the marker is attached (the target of the attachment), で marks the red ribbon as the means or material used for marking. 目印 ('mark, sign, identifier') + 付ける ('to attach, fasten') = 'to put a mark on, to add an identifier.' A small everyday move — making your umbrella distinguishable in a crowded umbrella stand at a station or restaurant.