How to take level 6 territory nonfunctioning quarry, like how can I keep taking higher levels of territory?

For each higher level of territory you will need to increase your loyalty in the event and also have a strong enough legion to win the fight to occupy it. Loyalty is increased by upgrading the Coalition Base camp structures. Harvest the materials from the farm, ale and quarries plots in RoC, then process this in the Frontline workshops. Keep doing this to gain the materials to upgrade your Coalition basecamps.