The time t that a random walk occurs is proportional to the number of steps taken during the random walk simply because the rate of collisions between particles, on average, does not change in time. considering the trend you found in the previous question of how the average values of the displacement ⟨ δ x ⟩ and displacement squared ⟨ ( δ x ) 2 ⟩ are related to the number of steps taken, and the relationship between number of steps and time, the equation of motion for diffusion would necessarily state that where the symbol ∝ means "proportional to".