This is a tough question, because the right answer relies on understanding the meaning of the object of a transitive verb and what prepositional phrases can go with a verb.
To "acquaint" is to inform. The object of the verb is the person who is gaining the knowledge. So I can "acquaint you" with information.
To "illustrate" is to show something. But the object of the verb is the thing being illustrated, not the person that it is being illustrated to. If I say that I will "illustrate you", that means that I will show pictures OF you, not show pictures TO you. Or it could mean that I will draw pictures on your body, like a tatoo artist. If I am going to "illustrate you with" something, like here, the second meaning would apply: I am going to draw pictures of the problems on your body. Extremely unlikely that this is the intended meaning.
To "convince" is to persuade. The object is the person (or organization or whatever) being convinced. So yes, I could "convince you" of something about these problems. But when we use the preposition "with", then we are saying HOW we will convince you. I might say, "I will convince you with logical arguments" or "I will convince you with personal testimony". It is unlikely that the problems of the society members are the means by which someone will be convinced. It would be plausible to say, for example, "I will convince you of the seriousness of the problems faced by society members" or some such. But you must say "of" or "about" to say what you are trying to persuade the person to believe, not "with". It occurs to me, though, that in context "convince" could be a valid answer. Like, "Many people in our nation face problems trying to find suitable housing. You don't believe this is true? I will convince you with the problems faced by society members." That is, the problems faced by society members are an example that (I hope) will convince you that my previous statement is true. But it's an unlikely sentence.
"Demonstrate" has the same problem as "illustrate". The object of demonstrate is the thing being demonstrated, not the person who is witnessing the demonstration. I could "demonstrate this problem to you", but I can't "demonstrate you this problem". To "demonstrate you" would mean that I am showing you to an audience, like you're a robot who I will run through its paces for the audience.
So the only word that really fits is "acquaint".