Explanation:

- "because": This word indicates a reason or cause. It doesn't fit the sentence structure, as we're not explaining why she was walking in the garden.

- "provided that": This phrase introduces a conditional clause. It implies a condition or stipulation that is not present in the sentence.

- "so that": This phrase indicates purpose or intent. The sentence does not express a purpose for finding the flower.

- "while": This word indicates simultaneous actions, which fits the context of the sentence as her walking and finding the flower happen at the same time.

Your Answer: 4 - while