which bus route can we take from royal park hotel to ngong ping 360?

Yes, from 7th Sep. to 24th Sep., the cable car will be under restoration. So you need to take the bus instead.
There is no direct bus mode, you need to transfer. Take the bus E42 from the hotel to Tung Chung Fire Station, and then walk to the opposite of the street to Yu Tung Court to take the bus No. 23 to Ngong Ping directly. The bus fare is HKD31.1in total, and the travel time is about 115 mins.