(i) To find the number of different arrangements of 6 pegs, all of different colours, in 4 holes, we use permutations. The number of ways to choose 4 pegs from 6 is given by the permutation formula:

\(^6P_4 = \frac{6!}{(6-4)!} = \frac{6!}{2!} = 360\)

Thus, there are 360 different arrangements.

(ii) For 4 pegs consisting of 2 blue pegs, 1 orange peg, and 1 yellow peg, we need to account for the repetition of the blue pegs. The formula for permutations of multiset is:

\(\frac{4!}{2!} = 12\)

Therefore, there are 12 different arrangements.