I will stop over in Hong Kong on my way to Taiwan, and in my way back I will do a tour in China. Do I need a single or a double-entry visa?

Hong Kong and Mainland China apply different exit & enter controls. Maybe you don't need a visa to Hong Kong, can you tell me your nationality? Chile passport holders are exempt from a visa to Hong Kong for up to 90 days. You need a single entry visa to Mainland China.