Communicate effectively with others using the language of the discipline and that of educated public discourse.

that 是个“替代词”，为了避免重复，替代前面的 the language。using 后面是两种不同形式的语言，由 and 连接。用了 that， 避免再次使用 the language。

that of educated public discourse：受过教育的公共语言。

此为祈使句，网友多读几遍，就找到感觉了。