If you go and review film and or notice while watching the games, you'll see that Jeff Carter is cleary more effective offensively when working from the left side versus the right. If you look at what Jeff likes to do on the attack, it's either rush the puck up ice and unleash the wrister or take the puck off the wall or from behind the net, loop around to the circle and fire on net. In both cases he's more effective when doing this from the left side than from the right.
Look at the two goals Jeff has scored this year. Both were against Colorado and both came from the LEFT side. His first came after making a strong defensive play on the left side, racing toward center then finally deeking to the backhand and scoring. His second goal game when Richards slid a pass to the LEFT side and Jeff backhanded it in. Unfortunately, playing on the right wing, Jeff doesn't get many chances to cross over and play from the left...and if he stays on the right, his angles aren't as good. Indeed most of the shots he's making from the right side have been easy saves for the opposing goalies.
Look at Carter's goal videos from the link below. Notice how many goals he scores from either the left side (especially with that wicked wrister from the left circle) or the center position. Meanwhile, Jeff has little to no (non empty net) goals scored from the right.
Also, here's an example from the recent game in Philly against the Pens that illustrates how Carter struggles coming out from the right side...
Notice he cannot readily get into good shooting position off the backhand here...he ends up getting off a weak shot from long distance. If he was coming off the left side he'd be on the forehand as he came around and could easily get into that scoring position in the left circle where he's been most lethal.
I reiterate, If Jeff Carter has to play wing, then I think it would behoove the Flyers to make it the LEFT wing instead of the right. Maybe JVR can play his off wing on that line too? Heck, it worked nicely on that goal in Colorado.