If one thing suggests another, it implies it or makes you think that it might be the case.
The old picture suggests me the past I never forgot.
He suggested that is a plot or bait, but not an opportunity.
The last report suggested the place and time of the next meeting.
If you?imply?that?something is the case, you say something that indicates that it is the case in an indirect way.
The exports in June rose 1.5%, implying that the economy was stronger than many investors had realized.
I thought I never implied you can do anything unethical.
The market of this kind of product is pretty well, which implies more fierce competition.
If you intimate something, you say it in an indirect way.
The phenomenon in picture is just a social microcosm, but it intimates the worst problem that should draws all attention.
What did he intimate in his words just now？
He looked at me. I know that intimate me leaving.
If you say that someone insinuates that something bad is the case, you mean that they say it in an indirect way.
Her article insinuates it is likely that the official was alleged embezzlement.
What made him anger was that she insinuates about his personality.
The words sound like compliment, but in fact, it insinuates unhealthy practices in society at present.