From the Amanaki Outpost you can find this mission sitting on the Bulletin Board near the entrance of the town. You are to track down a number of rabid dogs and kill them with the provided shotgun. This means you need to head over to the marked area of the map, collect the shotgun and deal with the dogs.
Head to the West from the Outpost using one of the various vehicles found around there. The first is just across the bridge from the Outpost. When you get there you will find a crate of ammo and a shotgun. Swap your present weapon for the shotgun then climb the nearby vines. Start moving over to the West and enter the search zone to start looking for the 5 rabid dogs that need to be dealt with.
Once you get into the search zone, head for the second objective marker. As you close in on it you will find yourself set upon by 5 rabid dogs. They will attack Jay without any provocation at all.