、。
I had to shift my Rome hotel reservation by three days.
Literal
Rome [possessive-の] hotel [possessive-の] reservation [object-を], three-days shift-[must-なければならなくなった].
ずらす ('to shift, to slide over') is the transitive verb for moving a date or schedule — not cancel, just slide. ３日ずらす means 'shift by three days.' ~なければならなくなった ('came to have to') stacks obligation (なければならない) with change-of-state (なる) and past (た) — the need arose after something changed.