Carcillo earned the suspension in Game 3 of the Eastern Conference Final during a brief altercation with linesman Scott Driscoll, who saw Carcillo "kind of make his way toward the fight" and grabbed him to prevent a third man in situation.
As you can see, there's a half-hearted punch, and a slash, of sorts, then an elbow to the face as the pair comes away from the boards. That was originally called abuse of officials, which carries a 10-game ban.
But the league decided it wasn't quite abusive enough to be called abuse. From a release:
Carcillo had originally been assessed a suspension under Rule 40.3 for deliberately applying physical force to an official. A violation of that particular Rule requires a minimum suspension of “not less than ten (10) games.”
After considering Carcillo’s appeal during a hearing at the NHL’s New York office on Friday, May 30, the Commissioner ruled that Carcillo’s actions were more appropriately deemed a violation of Rule 40.4 for deliberately applying “physical force to an official for the sole purpose of getting free of such official during or immediately following an altercation.” The Commissioner determined that as appropriately re-classified under Rule 40.4, and under the totality of the circumstances, a suspension of six (6) games was the proper penalty.
Basically, Gary Bettman determined that the physical contact between Carcillo and the linesman was inadvertent on Carcillo's part.
In the full judgment, Rangers' Assistant GM Jim Schoenfeld's expert testimony seems to have made some difference. Schoenfeld argued that Driscoll was a big strong guy, and "if you're trying to get loose of a big strong guy, there are a lot of moving parts. It's not easy to break a grasp... I'm pulling here, I'm pushing there. And I think that's what happened. That's when the elbow came up."
Furthermore, he observed that Carcillo "just kind of melted" as soon as he realized he'd struck the linesman.
Bettman went for it. "I thus conclude that the application of physical force was 'solely for the purpose of getting free of the official," he wrote in his summary judgment.
With that, Carcillo is now eligible to rejoin the Rangers for Game 4, just in time to help them stave off the sweep. (We kid. This could go five.)