[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.