How to get the great wall and summer palace from hotel holiday inn express minzuyuan in Beijing

The closest subway station to your hotel is Beitucheng Station.
From your hotel to Great Wall, I think you reach Beitucheng Station first. At this station, you can take the subway line 8 to reach Gulou Dajie Station where you can change to line 2 to reach Jishuitan Station. From this station, you can walk to reach Deshengmen Bus Station. At Deshengmen, you can find frequent buses 919 to reach Badaling Great Wall.
To reach Summer Palace, you still need to go to change to subway line 2 first and take the line 2 to reach Xizhimen Station. From there, you can change to line 4 to reach Beigongmen Station. Get out of the station, you can see the Summer Palace.