The mean of a set of numbers is calculated by dividing the sum of the numbers by the number of numbers. In this case, the numbers 5, 8, 6, and k occur with frequencies 3, 2, 4, and 1 respectively, so the sum of the numbers is 5 x 3 + 8 x 2 + 6 x 4 + k x 1 = 15 + 16 + 24 + k = 55 + k. The total number of numbers is 3 + 2 + 4 + 1 = 10, so the mean is (55 + k)/10.

Since the mean is given to be 5.7, we can set this expression equal to 5.7 and solve for k:

(55 + k)/10 = 5.7

55 + k = 57

k = 2

So, the value of k that makes the mean of the numbers equal to 5.7 is 2.

Therefore, the correct answer is C. 2.