7. In The Importance of Being Earnest, what leads Algernon to suspect that Ernest/jack is a Bunburyist?

~Algernon finds a handkerchief emboidered "Jack Worthing" in his friend's jacketpocket.
~Gwendolen tells him that his name is really Jack.
~He overhears him call himself Jack to a friend.
~He sees an inscription on a cigarette case.

It's D.

which expect from "Flowers for Algernon" shows that Clarie starts to view himself differently as he becomes smarter?

In The Importance of Being Earnest, Algernon suspects that Ernest/Jack is a Bunburyist because he sees an inscription on a cigarette case. To understand this, we need to look at the plot of the play.

Algernon discovers a cigarette case left behind by his friend Jack. When he opens it, he finds an inscription that says "From little Cecily, with her fondest love to her dear Uncle Jack." This raises Algernon's suspicion because Jack has always presented himself to Algernon as Ernest, not as Jack. Algernon realizes that Jack might be leading a double life, using the name Ernest in town and Jack in the country.

To answer your question, Algernon's suspicion about Ernest/Jack being a Bunburyist is triggered by seeing the inscription on the cigarette case. This evidence suggests that Jack has been pretending to be someone else (Ernest) in order to lead a different life and escape obligations.

If you had read the play, you would know the answer. Without having read it, you fail the question.