If you've reached the deep caves where the red slime dragons attack, you need to interact with certain things in the cave. Check the vines on the right, then the broken wood on the left, then go back to the right...
you know after take a carve knife for Kuno. Where after I can fine him? I had big problems with it.
Have you been down to the cave with the red and green slime dragons? You'll find the knife down at the bottom of this dungeon.
After you find it, return to the quest building and talk to the Auxiliary Commander. He will help you complete the quest.