The correct option is (c) AN
AN EDUCATED MIND CAN TEACH MANY.
('An' is used before words beginning with a vowel sound; 'educated' begins with a vowel sound /e/.)
The article 'an' is used before words that begin with a vowel sound. Since 'educated' starts with the vowel sound /e/, 'an' is the correct choice. Options 'a' and 'the' are incorrect because 'a' is used before consonant sounds, and 'the' is used for specific/known nouns. 'This' is a demonstrative adjective and does not fit the slogan structure.