How do I get the number of displays in windows?

As you have discovered, EnumDisplayMonitors() will do the job but it is a little tricky to call. The documentation states:

The EnumDisplayMonitors function enumerates display monitors (including invisible pseudo-monitors associated with the mirroring drivers) that intersect a region formed by the intersection of a specified clipping rectangle and the visible region of a device context. EnumDisplayMonitors calls an application-defined MonitorEnumProc callback function once for each monitor that is enumerated. Note that GetSystemMetrics (SM_CMONITORS) counts only the display monitors.

This leads us to an easier solution: GetSystemMetrics(SM_CMONITORS). Indeed this may be even better than EnumDisplayMonitors() if you have psuedo-monitors.

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As illustration of calling EnumDisplayMonitors() try this:

BOOL CALLBACK MonitorEnumProc(HMONITOR hMonitor, HDC hdcMonitor, LPRECT lprcMonitor, LPARAM dwData)
{
    int *Count = (int*)dwData;
    (*Count)++;
    return TRUE;
}

int MonitorCount()
{
    int Count = 0;
    if (EnumDisplayMonitors(NULL, NULL, MonitorEnumProc, (LPARAM)&Count))
        return Count;
    return -1;//signals an error
}

Not tested, but essentially you only need to provide the callback for the enum function:

int numMonitors = 0;

BOOL CALLBACK MonitorEnumProc(HMONITOR hMonitor, HDC hdcMonitor, LPRECT lprcMonitor, LPARAM dwData)
  {
  //lprcMonitor holds the rectangle that describes the monitor position and resolution)

  numMonitors++;
  return true;
  }

int main()
  {
  EnumDisplayMonitors(NULL, NULL, MonitorEnumProc, NULL);
  }