can i travel from guangzhou international airport to zhengzhou by coach and how often they run and cost

Oh, it is a long distance between the two places, around 1,158km by road.

I'm afraid there is no direct bus from the airport to Zhengzhou, but you can catch airport shuttle bus linr 1 to CAAC Ticket Office near Guangzhou Railway Station, near which is the Provincial Bus Station. There is a direct long-distance bus to Zhengzhou leaving around 11:35. The bus fare is CNY200 per person.