from yantai (shandong) to zhengzhou (henan)

There is no direct planes between the two places. If you want to take planes, it is suggested to fly to Beijing and then take bullet trains or take planes to reach Zhengzhou.
Or you can take trains to reach ZZ directly, but there are only two trains between and for the detail train information you can refer to https://www.travelchinaguide.com/china-trains/.