I would like to take bus no. 6 from the city to Zhangjiajie national forest park.

Well, the bus line 6 doesn't run to the national forest park. But you may take a bus to the park from the Central Bus Station near the railway station. There are many departures at an interval of about 10 minutes. The trip takes about 40 minutes. I remember that the first bus departs at 6:30, and the last bus departs at around 18:00.