I need to travel from Linyi to Taizhou,what would be the best method and the approximate cost

There is no direct buses or trains between, so it is suggested to transfer in Nanjing.
From LY, there is one train between LY and Nanjing, K2502/K2503 and it takes about 11 hours. If you can book a sleeper, it is suggested to take the train. Upon reaching Nanjing, you can take a taxi to Nanjing East Bus Station to take the direct buses for Taizhou.
Or from LY, you can go to the LY General Bus Station to take the direct buses for Nanjing Zhongyangmen Bus Station. Then take a taxi for Nanjing East Bus Station.