After accepting this quest, fly out to Razorthorn Rise. This region is directly on the border between Terokkar Forest and Hellfire Peninsula, up in the mountains. If you cant find it, just look at the picture above.
This is similar to the quest I Was A Lot Of Things... from Shadowmoon Valley, in that you need to use some local beasts to dig up your plants for you. Luckily, you don't need to rely on the intelligence of some dumb pig that gets massacred by all of the nearby monsters and turns on you if you accidentally hit an AOE. You get to control the Ravager you'll use to dig up your five required Razorthorn Roots.
How do you control them? Easy! Kill the nearby Flayers until one of them drops a Razorthorn Flayer Gland. Target a Ravager, and throw it at them. Ta-da! They are now your pet! Hunters, Warlocks, you'll need to dismiss your real pet before doing this or it won't work.
Now, clear around the dirt mounds you see laying about, and use the pet command called Expose Razorthorn Root. Loot the root like you would loot any similar item. Collect a total of five, and you win! Return to Quel'Danas and collect your prize of 9 gold, 10 silver, 350 Shattered Sun Offensive reputation and a Shattered Sun Supplies pouch.
When the Alchemy Lab has been completed, this quest is replaced with Rediscovering Your Roots and retains the same objectives and rewards.