Mind being a little more clear? Battlewardens issue Behest quests and should start whenever the NPC tells you. Your goal is to kill the specified amount of mobs until the event ends, after which you'll be given a gil reward.
At least I assume that's what you're asking.
Naiya | Mithra | Windurst | Rank 10 | 1st Lieutenant | Ragnarok
WAR: 75 MNK: 75 SAM: 66
RotZ: O | CoP: O | ToAU: O | Apoch Nigh: O
Naiyah | B.Elf | 85 Rogue | Stormscale
Doubleday | B.Elf | 85 Paladin | Stormscale