Suggestion

Something suggested (with subsequent adposition being for)

"I have a small suggestion for fixing this: try lifting the left side up a bit."

The act of suggesting.

"Suggestion often works better than explicit demand."

Something implied, which the mind is liable to take as fact.

"He's somehow picked up the suggestion that I like peanuts."

The act of exercising control over a hypnotised subject by communicating some belief or impulse by means of words or gestures; the idea so suggested.