The answer is anagen. Milady names anagen — also called the growth phase — as the stage where new hair is actually produced, with new cells manufactured in the hair follicle faster than at any other phase.
Catagen and telogen are the other two named phases of the same three-phase cycle (transition and resting, respectively), while androgen isn't a growth-cycle phase at all — it's a hormone category, included here as a plausible-sounding distractor that tests whether students confuse hormone terminology with cycle terminology.
Milady Standard Barbering, 6th ed., Ch. 10 (Properties and Disorders of the Hair and Scalp), p. 256: "During the anagen phase, or growth phase, new hair is produced. New cells are manufactured in the hair follicle."
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