In The Godfather, Michael Corleone meets with Carlo, and tells him that he would be sent to Las Vegas and kicked out of the family for his involvement with another family.
Carlo gets into a car that Michael had waiting for him, thinking that it was for the ride to the airport. However, Clemenza was in the backseat and garroted Carlo from behind.
Why did Michael order for this to happen, when he could have just killed Carlo any other time?
Why did he tell Carlo that he was going to Vegas?
You've asked two questions but they are kind of connected.
Taking the last one first...
Why did he tell Carlo that he was going to Vegas.
At this point Michael is almost certain that Carlo was involved in the plot to kill Sonny but he needs Carlo to confess to make absolutely sure.
So he convinces Carlo that, even though Carlo was involved, nothing bad will happen to him and that even if he's out of the crime business he'll still have a respectable job with the Corleone family. Recall that Michael is moving his family interests to Las Vegas.
Barzini's dead. So is Phillip Tattaglia -- Moe Greene -- Strachi -- Cuneo -- Today I settle all Family business, so don't tell me you're innocent, Carlo. Admit what you did.
Come on. Don't be afraid, Carlo -- Come on, you think I'd make my sister a widow? I'm Godfather to your son, Carlo.
No Carlo, you're out of the Family business, that's your punishment. You're finished. I'm putting you on a plane to Vegas --
Of course, once Carlo confesses he has given Michael what he wants and signs his own death warrant.
Why did Michael order for this to happen, when he could have just killed Carlo any other time?
Well this is true, Carlo could have been killed at any time afterwards but this is the day that Michael closes the books on his enemies (see the bold part of the quote above). The whole day is a sequence of Michael's enemies and people responsible for offences against the Corleones to be killed.
The first opportunity for Carlo to be killed is on leaving the Corleone compound, ostensibly to be taken to the airport to fly to Vegas. He gets into the car willingly, having been taken in by Michael, and is immediately executed.
The car then becomes a mobile, contained, crime scene and there is no evidentiary connection to the Corleone compound.
Certainly, Michael wouldn't want a murder to take place inside his house so taking Carlo out in the car makes it "cleaner" all round.
