how to get Great Wall from Sunworld Hotel-Dengshikou, Dongcheng by Public transport ??

Do you refer to Badaling Great Wall?
If yes, you can take subway line 5 at Dengshikou Station, get off at Yonghegong Station. Then transfer to line 2 to Jishuitan Station.
After arriving, walk to Deshengmen Station and take public bus no. 877 to Badaling Great Wall directly. The whole cost is around CNY 20 per person.

Or you can take subway line 5 to Yonghegong, then change to line 2 to North Railway Station. There are several trains that can take you to the Badaling Station. Then walk to the scenic area directly. You can search the schedule on this website on your own.

If by taxi, the cab fare is CNY 300 to 400 for a single trip, or even higher for the return no-occupancy surcharge. But I'm afraid it's hard to hire a taxi for the long distance. If insist, you can use the car rental service of this website, which will be much easier. The contact info is traveltravelchinaguide.com