。
She asked the front-desk clerk to put her through to that number.
Literal
She [topic-は] hotel's front-desk-clerk-person [to-に] that number [to-に] connect [in-such-a-way-ように] requested.
This sentence has a stack of dative に — one for the requested person (フロント係の人に, 'to the clerk'), one for the connection target (その番号に, 'to that number'). Each fills a distinct role: addressee of the request, and end-point of the connection. The set フロント (loanword from English 'front,' meaning hotel front desk) + 係 ('person in charge') + の人 ('the person') is a politely overspecified way to say 'the front-desk clerk' — a triple layer that softens the reference. This phrasing fits a formal service setting: phoning a hotel, asking to be transferred to a room.