Help! Is 6 days enough for hydrocodone to be out of my system for a urine test?

Depends on dose. In very high doses, it may still be present if you are tested by a very sensitive method, but if it was lower dose and one-time use, it would likely be negative after six days. However, if you are using hydrocodone without a prescription DESPITE being subject to drug testing, I would wonder if you have a real drug problem. Worry more about that than getting caught and you will be better off.
Narcotic tests. Concern of a work related narcotic test (urine or serum) is itself a warning sign of potential addictive use. If the prescribed narcotic is legitimate, the use can be disclosed to the employer/testing entity and will not be an issue. .