Me, being a lefty (hence my board name), Would have the heavier item in my right hand (beer) and the precious/lighter cargo (wings) in my left.
Assuming the beer is cheap stuff it would be carried below your waist to help relax your arm.
The wings would be carried above waist line to keep them level and so you can smell them until you get home.
Scenario: Walking down the street after leaving the liquor store you begin to cross the street towards an alley on your left. As you begin to pass the alley you look down the alley to see a knife weilding bad guy running towards you [Help]!!! You must think quick because he is moving towards you at a very fast rate of speed. With the beer in your right hand you would chuck the 12 pack at his head! Assuming the BG has half a brain he would either duck or it would be in your favor if he took it straight to the melon! Well since he is a hardened criminal and this is not his first rodeo he dodges the beer [Mad]. At this time he is somewhat distracted and now is your time to strike![M2]
This next part is where it gets complicated [Luck]. You now have about 3-5 seconds before certain death is upon you. With the wings in your left hand you toss them straight up in the air. While the 18 delicious Mango Habanero wings from BWW[Lick] are in the air ,you draw your "Dirty Harry", take the shot [AR15], stop the threat, reholster, and catch the wings before they hit the ground [Wow2] Since the beer would be in cans (my prefence when I am going cheap), you can now go scavenge up the beer. Hopefully the box didn't break but even if it did the beers would still be intact.
Now its time to [Phone] the [PoPo]
go home and [Pepsi][PizzaHut]