8) C

In order to return to the same position, a player has to land on the opposite direction but the same distance.

e.g. A player lands on Right and distance 2. In order to return to the original position, the player has to land on Left direction with distance 2.

Probability of landing on Left = ¼

Probability of landing on 2 = ¼

Probability of returning on the same position = ¼ x ¼ = ¹⁄₁₆