suggest vs proposition

suggest is not a noun while proposition is a noun.

Word	Noun	Adjective	Verb	Adverb
suggest	No	No	Yes	No
proposition	Yes	No	Yes	No

As verbs, proposition is a hyponym of suggest; that is, proposition is a word with a more specific, narrower meaning than suggest:

suggest (noun)	proposition (noun)
	a task to be dealt with
	(logic) a statement that affirms or denies something and is either true or false
	a proposal offered for acceptance or rejection
	the act of making a proposal
	an offer for a private bargain (especially a request for sexual favors)

suggest (verb)	proposition (verb)
make a proposal, declare a plan for something	suggest sex to
call to mind
imply as a possibility
drop a hint; intimate by a hint