My sister has . . . . . . . . H. B. A degree.

Use 'an' before words such as "hour" which sound like they start with a vowel even if the first letter is a consonant. Also use 'an' before letters and numbers which sound like they begin with a vowel, such as "F" or "8". Here H.B.A begins with a vowel sound and therefore 'an' article will be used.