This question tests your understanding of modal verbs and past necessity in English grammar. The correct phrase must indicate that packing towels was unnecessary in the past, and this lack of necessity was known before the action was considered or performed.

Let's analyze the sentence and the options step-by-step:

Step 1: Understand the Context
The clause "because we knew the hotel would provide some" tells us two things:

1. The event (considering packing towels) happened in the past.
2. We had knowledge beforehand that the action was unnecessary.

We need a verb form that expresses this past lack of necessity.

Step 2: Evaluate the Options

• Don't have to pack: This is present tense. It describes a general lack of necessity now or in the future, not a specific past event. It does not fit the past context of the sentence.
• Needn't pack: "Needn't" is a modal verb used for present or future lack of necessity. Like the first option, it is not used for past events.
• Needn't have been packed: This is the passive voice form of "needn't have packed". We use "needn't have + past participle" (e.g., needn't have packed) to express an action that was done in the past but was later understood to be unnecessary. However, this option is in the passive voice ("been packed"), which is incorrect because the subject "We" is performing the action (packing), not receiving it. The sentence requires the active voice.
• Didn't need to pack: This is the correct form. "Didn't need to" is used to express that an action was not necessary in the past. Crucially, it is used when the lack of necessity was known before the action was (or wasn't) performed. This matches the context perfectly: we knew the hotel provided towels, so the necessity to pack our own never existed.

Final Answer: The most suitable option is Didn't need to pack.
The complete sentence is: We didn't need to pack our towels because we knew the hotel would provide some.

Related Grammar Points & Theory

Expressing Past Lack of Necessity

There are two main ways to express that something was not necessary in the past. The choice depends on whether the action was performed or not.

1. Didn't need to / Didn't have to: This is used when the action was not performed because it was unnecessary. It can also be used when we don't know if the action was performed. The key is that the lack of necessity was known beforehand.
   • Example: I didn't need to buy milk. My roommate had already bought some. (I did not buy milk.)
2. Needn't have + past participle: This is used when the action was performed, but it was later understood to have been unnecessary.
   • Example: I needn't have bought milk. My roommate had already bought some. (I bought milk, but it was a wasted effort.)

Key Formula

To state an action was unnecessary and not done:
Subject + didn't need to / didn't have to + base verb + ...

To state an unnecessary action was done anyway:
Subject + needn't have + past participle + ...