how do i get to purple mountain from jiang kang road in Nanjing?

I wonder whether you mean Jian Kang Road. If so, besides taxi, I suggest you walk from Jian Kang Road to Changbai Street to take bus no, 55 to Zhongling Street Station, where take subway line 2 to Muxu Garden Station (Muxuyuan). Then you can take a taxi to reach the cable car station of Purple Mountain.