Explanation:

- We have six friends: H, I, J, K, L, and M, and holiday dates on 2nd or 5th of October, November, and December.

- Three people went between M and K. Therefore, M could be at the start or the end with three others between.

- M went after K, so M is at the end, placing K at the start.

- H went immediately after L.

- J went two places after M.

- I did not go in December, fixing I in either October or November.

Let's rearrange:

- Placing K on the earliest: 2nd October

- Consequently, M is on 5th December.

- J, two people after M, on 5th December, cannot hold. Thus, J must go 2nd December.

- L might be on 5th November, and H is on 2nd December.

- I is on 5th October.

With this configuration, J went on holiday on 2nd of November.

- J went on holiday on 2nd November.

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