Either Carrie or Maria ------ been writing the letter.
D
Correct answer
Explanation
With 'either/or', the verb agrees with the nearest subject. 'Maria' is singular (third person), so use 'has'. 'Either Carrie or Maria has been writing' means one of them (individually) has been doing it. Option A ('are') is plural, B ('is') would need 'has', and C ('have') is plural.