If someone is wondering: yes, the sentence has two different correct solutions.
[-] The woman admires the horse.
[-] The woman admires the horses.
Why? Because the declension of the noun 'anne' for nominative and accusative is as following:
anne (singular nominative)
anni (plural nominative)
annī (singular and plural accusative)
Given the fact that the horse/horses is/are the object of the sentence, the word will become annī. Cheers!