Step 1: Rule for indefinite articles before vowel sound.
We use an before words beginning with a vowel sound. Step 2: Application to “honorable.”
Although “honorable” starts with consonant letter ‘h’, the ‘h’ is silent in pronunciation, so it begins with the vowel sound /ɒ/. Therefore we use “an honorable man.”
\[
\boxed{\text{an honorable man}}
\]