proposition vs suggest

proposition is a noun but suggest is not a noun.

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

As verbs, suggest is a hypernym of proposition; that is, suggest is a word with a broader meaning than proposition:

Other hypernyms of proposition include advise, propose.

proposition (noun)	suggest (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)

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