To answer this question, we need to understand the concept of conditional sentences and the use of the third conditional.
The given sentence is in the third conditional form, which is used to talk about a hypothetical situation in the past and its hypothetical result. In this case, the hypothetical situation is the woman waving to him, and the hypothetical result is him seeing her.
Let's go through each option to understand why it is correct or incorrect:
Option A) didn't see - This option is incorrect because it is in the simple past tense, which does not convey the hypothetical nature of the situation. We need to use the third conditional form.
Option B) would not have seen - This option is correct because it uses the correct form of the third conditional. The auxiliary verb "would" is used to express the hypothetical result, and "have seen" is the past participle form of the verb "see."
Option C) would not see - This option is incorrect because it is in the present tense and does not convey the hypothetical nature of the situation. We need to use the third conditional form.
Option D) will not have - This option is incorrect because it uses the future tense, which is not appropriate for a hypothetical situation in the past. We need to use the third conditional form.
The correct answer is B) would not have seen. This option is correct because it uses the correct form of the third conditional to express the hypothetical result of the woman not waving to him.