Question

¿Dónde te cortaste el pelo? a. En el centro. b. Fui a la peluquería Doña Renata.

Answer 1

B) Fui a la peluquería Doña Renata. (This is the answer)
Because it's a place where you can get a hair cut.
and A) isn't specific .

Answer 2

Peluquería means hairdresser. the question asks where you get your hair cut, so B is correct