They can't possibly be both right and mean the same thing.
Do you mean you have to propose the idea acceptably, or that the idea you propose must be acceptable to the committee?
Naturally, the adjective qualifies the noun 'ídea' - and acceptable idea; and the adverb modifies the verb 'propose'.
You can propose an acceptable idea unacceptably. "Hey, dudes, you'll never guess what I thought of! - <insert acceptable idea>."
To save you some trouble, no two words ending in 'able' and 'ably' can mean the same thing. And this applies to most adjective/adverb pairs.
Student or Learner