If you need the object GRAPHICS *GE in a lot of files:

// main.h
// declaration of GRAPHICS. Some compilers will tell:
// "warning C4091: 'typedef ' : ignored on left of 'GRAPHICS' when no variable is declared"
// you can delete the 'typedef' in that case.
typedef struct GRAPHICS
{
  // ... whatever your GRAPHICS variables/functions are - goes here, as you know
};
// if you delete "typedef" then do NOT define a variable between the immediately preceding "}" and ";"

extern GRAPHICS *GE; // forward declaration for anyone needing to access GE

// main.cpp
#include "main.h"
GRAPHICS *GE = NULL; // definition

// don't where you create GE. But..
GE = new GRAPHICS; // instantiation

// any other header or cpp file that needs access to GE
#include "main.h"

// somewhere in the code in this cpp. Don't know how you use it, but..
int number = GE->GiveMeANumber(); // some use of GE

There's no rule that says you have to do it any particular way. It's just a good rule of thumb. You can put "extern GRAPHICS *GE;" in any header. Provided the definition "GRAPHICS *GE;" appears in only one place in all the compiled code, the linker will find it.

As rip-off mentioned, each #include header is "pasted" into a cpp file before it's compiled, and each cpp is compiled separately into a separate obj file. Then the linker combines all the obj files into a single executable. If "GRAPHICS *GE;" appears in a header file that's included in (say) 2 cpp files, the linker ends up with something that looks like:

GRAPHICS *GE; // from one obj file
GRAPHICS *GE; // from another obj file

And, as you know, you can't have 2 variables named the same in the same space. That's where your original errors were coming from.