The answer is 4 to 5 months. Milady states this as a direct fact in its hair-loss section: eyebrow hairs and eyelashes are replaced every 4 to 5 months.
It's worth not confusing this with the book's separate figure for normal daily scalp-hair shedding, which it lists as 75 to 100 hairs per day (one of this question's own distractor choices, repurposed from a different statistic). Eyebrows and eyelashes cycle on their own, much shorter, growth-and-replacement schedule than scalp hair.
Milady Standard Barbering, 6th ed., Ch. 10 (Properties and Disorders of the Hair and Scalp), p. 256: "Eyebrow hairs and eyelashes are replaced every 4 to 5 months."
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