Are you trying to run MinGW under a linux emulator? You probably don't have permissions to run MinGW from within c:/users/mat folder. Move MinGW to C:/MinGW then make sure to grant access to everyone then try again.
@AD: That's a screen shot of msys, the MinGW replacement from cmd.exe (command prompt). It is a unix-like bash shell for Windows, like cygwin. That's the standard way to run MinGW/GCC in command-line (unless you want to suffer and use the command prompt).
@Vastor: The problem I see on the screenshot is that you are using a DOS-style address of the folder, but msys (or cygwin) uses Unix style. In other words, you entered
cd C:\Users\mat, but, in Unix style, it should be
cd /c/Users/mat. That's all. It might be good to for you to know a few basic Unix shell commands.
There shouldn't be an access rights problem here, since you are the user "mat", and if there is, it will display a message saying that. It is usually preferable to avoid user directories in Windows, they are a mess of access restrictions and convoluted symbolic links.