By the time we arrived, all the food _______ by the guests.

The correct option is c.

The sentence describes an action that was completed before another past action. "We arrived" is in the simple past. The eating of the food happened before the arrival. This requires the past perfect tense.

Additionally, "all the food" is the recipient of the action (it was eaten), so the sentence needs to be in the passive voice.

• Past perfect active: had + past participle (e.g., "The guests had eaten all the food.")
• Past perfect passive: had been + past participle (e.g., "All the food had been eaten by the guests.")

Let's examine the options:

• a. "had eaten" - This is past perfect active. It would mean the food itself performed the action of eating, which is incorrect.
• b. "was eaten" - This is simple past passive. It implies the food was eaten at the same time or after the arrival, not before.
• c. "had been eaten" - This is past perfect passive. It correctly indicates that the food was eaten before the arrival.
• d. "had ate" - This is grammatically incorrect. The past participle of "eat" is "eaten," not "ate."

Therefore, the correct completion is "had been eaten."

The complete sentence is: "By the time we arrived, all the food had been eaten by the guests."

The final answer is $\boxed{\text{c}}$