These quests have to go to a city and steal a set of gold's worth of items. You cannot be seen stealing the item. Any items taken like that will not count toward your total. If you are put into jail or placed under arrest then the quest will fail.
To complete this job, take your time. The best time to work is at night. Most people will be asleep. You can simply break into shops and steal goods from there to quickly complete the job. You can also head into the Wealthy Houses and steal appropriately valued items.