The meaning of ‘How’ in this conversation
In a non-academic way. The use of 'How' in this sentence proceeds further context.
Ill explain using your example.
1: Do you remember when we invited people to our house last month?
2: Of course, That was so much fun.
1: And you remember how Alice and John Brought over their kids?
2: Yes?
- 1: Well they've invited us this weekend and i thought we should bring ours.
When you use How in reference to a past event like that, the insinuation is that you'll be elaborating on the instance you are referring to. In this example, 1 is using how to refer to an instance of event where someone did something as a justification for doing it themselves now. Otherwise if you were just referring to the past action it would look like this.
- 1: Do you remember when we invited people to our house last month?
- 2: Of course, That was so much fun.
- 1: I really didn't like that Alice and John brought their kids.
Although even in this context you could easily use how instead and it would still make sense, I'm not sure it's technically correct, but it's interchanged commonly in normal spoken English. I think it's slang that's just become so commonly used that it's considered normal perhaps.
//Someone: Do you remember we invited people to our house last month? Me: Of course. That was so fun. Someone: And you remember {how} Alice and John brought over their kids?//
When you ask, "...And you remember how Alice and John brought over their kids?" it may connote 'your/and other participants' experience - good or bad - with the kids'. When you ask "...And you remember that Alice and John brought over their kids?" it may imply, "...you never thought they would bring/ or you surely thought so...; you are (not) happy at their coming; as if something that you expected 'about the kids coming' happened. For this, the second sentence should end in an ! mark. It is sure that WHAT and HOW are not interchangeable; they have different implications.
Additionally, "how" can potentially refer explicitly to explicitly the manner of how someone does sth. Especially if emphasized in speech.
Someone: Do you remember that Alice and John brought over their kids from the GDR?
Me: I do. That must have been 50 years ago.
Someone: And do you remember how Alice and John brought over their kids?
Me: Now that you mention it, yes! They smuggled them over the intra-German border on the back of the army truck, didn't they?!
Using 'how' like this usually emphasises the unusual, entertaining, inappropriate or embarassing nature of the action. In this case 'how' refers to the result of the action rather than the process by which it was achieved.
Consider "Remember how John got drunk at his ex-girlfriend's wedding." In this case the speaker is not talking about the exact number of glasses of wine, beer and spirits that John consumed or the way in which he consumed them (which could have been openly, furtively, noisily and so on) but refers to the way he acted when he was drunk. Whatever he did would have had a negative impact on the poor girl's big day and the use of 'how' emphasises that impact.
Using the alternative "Remember that John got drunk at his ex-girlfriend's wedding" has a very different emphasis. In this case it is more of an instruction to take the fact into consideration when planning a future action. It might be a warning not to invite John to a party where the ex-girlfriend and her husband were on the guest list.