Acheter = To buy
Emmener = To bring
J' [blank] ma mère à l'hôpital. - "I [b l a n k] my mother to the hospital."
You didn't buy her to the hospital, you brought her to the hospital. Verbs ending in -ons are the conjugation for nous. The pronoun in question is j' or "I", so the correct conjugation is emmène. J'emmène ma mère à l'hôpital.
Answer:
b. emmène