。
When did she promise to meet him?
Literal
She [topic-は] he [to-に] when meet [that-という] promise [object-を] made [explanatory question-のですか]?
A clause-internal relativizer in action: いつ会う ('when they meet') is a complete proposition, nominalized via という, and used to specify the content of 約束 ('promise'). 彼に most naturally attaches to 約束をした ('made a promise to him'), though it could parse as a piece of the inner 会う clause. The closing ~のですか is the polite explanatory question, asking for the backstory.