The logging option to enable binary log index file is . . . . . . . .

This question is asking about a MySQL option that turns on a special file called the binary log index file. This file helps MySQL work more efficiently when dealing with transaction logs.

Let's look at the options:
* Option A: -log-bin-index - This option is the correct answer. It tells MySQL to create and use the binary log index file.
* Option B: -bin-log-index - This is a close call but the correct order is log-bin-index
* Option C: -index-log-bin - This is incorrect because the order of the words doesn't match the actual option name.
* Option D: -index-bin-log - This is also incorrect for the same reason as Option C.

So the answer is Option A: -log-bin-index