Mechanically, if Andy wants to compel an action from Mike, he should give Mike one of his Fate points. That also seems like the best way to handle it thematically. Also, using Intimidate to "give Mike a hard time" isn't really enough reason to compel a Fate Point in the first place, unless Andy is granting himself an extra +2 on his Intimidate die roll or if Mike concedes the roll because of Andy's invocation of the aspect.
The bottom line is: any time you use a player's aspects against him, they get Fate points for it. The only exception is if you have a free tag to use. Andy doesn't have that free tag, the ghost does. Unless you can justify in some what the ghost giving Andy the tag (and I'm not seeing it here), he has to spend the Fate point, and, as noted, give it to Mike.