Harry sits at lunch, chatting with Ron and Hermione about [Apparition] and Tonks's moodiness.

Trying to Catch Malfoy in the Room of Requirement
At breakfast, Harry talks with Ron and Hermione about ways to persuade Slughorn or get into the Room of Requirement, and they learn that Mundungus Fletcher has been sent to [Azkaban].
During his free period, Harry tracks back and forth in his Invisibility Cloak outside the Room of Requirement, trying to gain entry with no success.
Inferi Versus Ghosts
Snape starts Defence Against the Dark Arts class talking about the difference between Inferi and ghosts, mocking Harry for his simplistic definitions and taking points from Ron for talking back.
Ron and Harry, chatting about Inferi, run into Moaning Myrtle in the bathroom and she tells them that another boy has been in there crying.
Frustration Outside the Room of Requirement
As Ron and Hermione prepare to head off to [Hogsmeade] to practice [Apparition], Hermione and Harry talk about his difficulties cornering Slughorn and his inability to get into the Room of Requirement.
Harry spends another morning trying unsuccessfully to get into the Room of Requirement, though he does succeed in scaring off a [Polyjuiced] Goyle. Tonks soon comes by though, on her way to see [Dumbledore].
Chapter 22 - "After the Burial" - In which Aragog dies, Ron and Hermione have their apparition test, and Harry makes a Euphoria potion in a class with just Slughorn, Ernie and Draco, after which he tries to corner Slughorn but fails. Hermione passes her test and convinces Harry to take Felix Felicis to get Slughorn's memory; Harry does, and goes down to Hagrid's, meeting and inviting Slughorn along the way. There they bury Aragog together, Slughorn and Hagrid become drunk, and Harry convinces Slughorn to give him the memory.
One More Try for a Memory
On the morning of the [Apparition] tests, Harry, Ron, and Hermione sit in the courtyard - Ron working hard to avoid Lavender - when they get a letter from Hagrid saying that Aragog has died. Before leaving, Hermione convinces Harry to use his [Felix Felicis] if he can't get the memory from Slughorn in Potions class, and the [Montgomery] sisters walk by crying, strenghtening Harry's resolve.
In a Potions class with only Harry, Draco Malfoy, and [Ernie Macmillan], Harry brews [An Elixer to Induce Euphoria], but is unable to get Slughorn to take some and unable to convince him to give up his memory.