The Court found that Embody's 2nd, 4th, and 14th Amendment Rights were not violated when he was stopped in Radnor Lake State Natural Area while open-carrying a Draco AK-47 pistol. The Draco had an 11 1/2 inch barrel and had the tip of the muzzle painted orange much like an airsoft toy.
This case has been troublesome since the start due to Mr. Embody's hubris. To be frank, he went looking for trouble, found it, was momentarily detained, and then sent on his merry way no worse the wear. In response he filed a suit in US District Court for the Middle District of Tennessee. The end result of that was to have everyone's Second Amendment rights circumscribed due to that court's decision which misread the Heller decision.
As Judge Sutton of the 6th Circuit noted in his opinion:
For his troubles, Embody has done something rare: He has taken a position on the Second and Fourth Amendment that unites the Brady Center to Prevent Gun Violence and the Second Amendment Foundation. Both organizations think that the park ranger permissibly disarmed and detained Leonard Embody that day, notwithstanding his rights to possess the gun. So do we.Alan Gura had filed an amicus brief on behalf of the Second Amendment Foundation and the CalGuns Foundation that argued the District Court got the decision right but for the wrong reasons. It asked the 6th Circuit to affirm the decision but find that the Second Amendment didn't apply in this case. The appeals court seems to have agreed with this and said the Second Amendment didn't apply in this situation due to qualified immunity.
Sebastian at Shall Not Be Questioned has much more on the decision here. The Volokh Conspiracy also covers the decision and there is a lively discussion going on in the comments section.
Whether or not Mr. Embody decides to appeal to the Supreme Court is up to him. If he does, I'd wager house money that the Supreme Court would deny certiorari in this case.