At least it is with good reason that Rykhar is sending you out to kill Zal'kuk Warriors. Helping fellow dragons is always a good thing, and if you can learn more about your own abilties at the same time, then that's a bonus!
Travel to northern Char, along the coastline in particular, and defeat 20 of the Zal'kuk Warriors in order to discourage them from coming too close to any dragon settlements.
Return to Rykhar for your reward
I know you may not enjoy hearing this, but there's a group of ogres that are causing some real problems in northern Char. Char is an important region of the world for dragons, for many build their lairs within the volcanic mountains that make up this region. It is not just that, however. Char is, of course, the area around Dralk itself and thus should be protected as best we can. Though the Fire Ogres are not yet close to any particular settlement or to our city, they tend to roam and spread out the longer they are left alone. So I'd like you to travel to northern Char and kill some for me. There's no real study in this task, I just need someone to teach these ogres they can't bother us.