K8 is an immediate neighbor of both K4 and K6, who faces towards the center. K3 sits third to the right of K6 so, either K4 sits to the left of K6 or in the right of K6. Case I: When K4 sits to the right of K6. 
Case II: When K4 sits to the left of K6. K2 sits 3rd to the left of K3 so, case II is invalid, because K2 can’t be placed in case II. 
K1 sits second to the left of K2, K1 faces the same direction as K6. Immediate neighbors of K1 face the same direction. K2 sits 3rd to the left of K3. K4 and K2 face opposite directions. Immediate neighbours of K6 face the opposite direction as of K1. Neither K7 nor K5 is an immediate neighbor of K3. K5 doesn’t sit immediate right of K2. The second possibility gets eliminated as it is not possible to place K2 third to the left of K3. So, K2 faces towards the center. K1 and K6 also faces towards the center. The final arrangement is as follows: 
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