Ask him RS gold where you can get a symbol and he'll tell you the symbol maker is at the 2nd floor of the palace (which is below your floor.) Tell him to let you out and you'll get a symbol. You will be allowed out and the Mogre will direct you to the emblem maker, not letting you move. You will speak to the Yarg, the emblem manufacturer and he'll ask you what symbol you desire. You will be able to choose between Lannar: The Mogres of Weaponry and the Color Yellow, Lu'tog: The Mogres of Poison, Combat and the Color Red, Narran: The Mogres of Peace, Agility and the color Blue and Yun'lar: The Mogres of both Defence and the Color Green.
He'll then make you a symbol of the area you choose. Wear the symbol and you'll be able to pass in your region from the palace. To identify what region you belong to, just choose the door of the colour. If you aren't sporting the emblem or you're wearing the symbol but you don't belong to the region, the guards will stop you. You cannot un-equip your symbol while on your area.
Quest complete! Benefits: 7,000 magic XP, 12,000 strength and assault XP and access to Mogrin by speaking to Captain Murk to sail you there! (If you lose your emblem, talk to a guard outside of Mogrin to receive Buy OSRS Accounts one or even if you shed your orb, talk to Tarren to get it back)