Hello!
Manger is the infinitive meaning "to eat"; acheter is the infinitive meaning "to buy". The sentence is saying that "Sylvie and Sophie [blank] some flowers for Mother's Day." Surely they didn't eat some flowers, so they must have bought some flowers. Now let's look at the conjugation. When you are talking about more than one person, the verb will end in -ent (Ils dorment - "they sleep").
Therefore the correct answer is:
c. achetent
Hope this helps!