It's hard to tell in this photo. It appears that Wheeler Peak is out of the photo to the left. Wheeler Peak can be identified from the tops of neighboring high peaks (like Lake Fork, Kachina or Gold Hill). If you had aimed your camera toward Wheeler, Simpson Peak (and/or Old Mike Peak) would be identifiable.
If I remember correctly, this photo was taken from the summit of UN 12819 looking east/northeast. This peak is Pt. 12,728 which is between UN 12819 and Simpson Peaks. I think getting up and down this peak will be the most difficult portion of a loop hike from Kachina to Wheeler. These photos from Simpson Peak help to put things into perspective.