Concept:The correct phrase means withdrawing from a promise, decision, or commitment.
Explanation:The sentence requires a phrasal verb that shows someone failing to keep a promise or pulling out of an agreement.
"Backed out" is the standard expression used in this sense.
"Backed up" means supported or validated, which does not fit the meaning.
"Backed for" is not a commonly used phrasal verb combination.
"Backed in" means reversed into a place, which is also unrelated.
Thus, "backed out" is the most appropriate choice.
Answer:C. backed out