You go through Infernal Pass on the west side of the mountain on your way to meet Carmine.
Reach Infernal Pass
If you didn't add Infernal Pass as a Fly destination earlier, go west from Kitakami Hall, through Oni Mountain and Oni's Maw, until you reach the road sign. Follow the sign that points left to reach Infernal Pass.
Explore Infernal Pass
If you haven't already, check on the small sign near the south end of Infernal Pass to add that location as a Fly destination to your map.
On a hill near the small wooden bridge, you can find a TM118 Heat Wave.
Farther north, on the east side of the path, you can find a TM082 Thunder Wave.
Farther north, on a small hill on the east side of the path, you can find a TM107 Will-O-Wisp.
North of that, there is a large hill in the middle of the path where you can find a TM184 Vacuum Wave. There is also a Terastal Slugma on this hill.
Go northeast from the large hill and you eventually can find a TM041 Stored Power on a small hill near a red gate.
Go through the red gate and the path will lead you to the Crystal Pool.