I am really lost on this one, can anyone shed some light on this one

The back of the book said to denote the cosets but I don't really know how to do this?

that is what is confusing me too

=

By "denote the cosets" the book means to think as though you were doing computations in the extension field and just ignore the fact that you are actually talking about cosets. Example: Denote 1 + 2Z as just 1, because 1 = 1 in Z_2. It seems to be a notational convenience.