mingw32-g++.exe -o "C:\C-C++ Development\analog_clock.exe" "C:\C-C++ Development\analog_clock.o" -lbgi -lgdi32 -lcomdlg32 -luuid -loleaut32 -lole32 "C:\Program Files\CodeBlocks-EP\sdk\winbgim\lib\libbgi.a"
Linker settings:
Created new project with WinBGIm template, graphics only
Libraries: C:\Program Files\CodeBlocks-EP\sdk\winbgim\lib\libbgi.a
Other Linker options: -lbgi -lgdi32 -lcomdlg32 -luuid -loleaut32 -lole32
Your problem is that you try to link with libbgi.a twice. It's valid and sometimes it's necessary, but the way you do it causes the error.
You already provided a full path to libbgi.a in "Libraries". This should be enough.
But in "Other Linker options", you try to link it again, this time with "-lbgi". Using -l implies that the library is either in compiler search path or in a directory that you added to "Linker Search Directories" window. Since libbgi.a is not there, the compiler reports error.
The solution is easy: remove "-lbgi" from "Other Linker options" OR add "C:\Program Files\CodeBlocks-EP\sdk\winbgim\lib\" to linker search directories (note: you should avoid paths with spaces such as "Program Files").
And it's better to provide library names in "Libraries" section (gdi32, comdlg32, uuid, oleaut32, ole32) than in "Other Linker options" because it's easier and you may hit the issue of libraries order when linking (as you see, "Other Linker options" have a priority.