That being the case vs in which/that case
 

What´s the difference between these two phrases?

They are synonymous, more or less. You could translate "that/this being the case" as "Siendo eso el caso", and you could translate "in which/that/this case" as "en ese/este caso".

And in the following sentence why do they give just one answer correct!
You said you're moving to Argentina. ---------------YOU WONT BE NEEDING your Harley. Can I have it?
In which case
That being the case
The only explanation that I can find is the verb agreement. If I choose In which case I would say YOU WON´t need. Is that correct?

:twocents:That being the case has an air of the subjunctive about it, as if it were a variation of the less understood, be that the case. In which case expresses less doubt.

so verb agreement has nothing to do?

I don't believe verb agreement has anything to do with it. It's just two ways of saying the same thing, but one of which seems more subjunctive.

Given the two choices and the context you provided (thank you), only one answer sounds right to me.

The second sentence depends on another event occurring. We can tell that the prior event hasn't happened yet because of the tense being used in the second sentence.

"In which case" is used to indicate that the statement that follows is true if the possible situation just mentioned actually occurred (or actually exists).
Since the situation has not occurred, it seems out of place to refer to it as though it had.

Using "in which case" in this instance may be acceptable in some regions (or to some people), but to me it just sounds wrong. The only clear choice in my mind is to treat the event as something that hasn't occurred yet, and "that being the case" is the only transition that works (of the two given).

You could use "in that case" instead of "that being the case," but it wasn't an offering.

And what about punctuation?
If it was a comma, could I put in which case?

Remembering that 'in which case' is used when the event has occurred (exists), a comma precedes the clause, and it and what follows it go in the same sentence with what has occurred.

--

The correct punctuation for 'That being the case' (or 'In that case', which wasn't offered as a choice) is a trailing comma, because it introduces the event that follows.

You said you're moving to Argentina. That being the case, you won't be needing your Harley. Can I have it?

You said you're moving to Argentina. In that case, you won't be needing your Harley. Can I have it?