A "hanger" is when you launch a disk and it lands hanging off the back edge of the board (it must be the back, not the sides). This shot is tricky to pull off as the physics in the game are a little wonky when it comes to the edges of the board. Just play a few games of Shuffleboard trying specifically for this shot. It shouldn't take too long to get the speed just right. You must finish the round with the disk still hanging off the back edge to unlock the achievement. Just waste your remaining disks so that they do not knock your hanger off.