How many derangements of {1, 2, 3, 4, 5, 6} end with the integers 1, 2, 3 in some order

How many derangements of {1, 2, 3, 4, 5, 6} end with the integers 1, 2, 3 in some order

Can you please show me how to do it?
Thanks!

question is equivalent of asking how how many derangements are there of {4 5 6}
times the number of derangments of {1 2 3}

both have 3! possible arrangements, so the answer is 3! * 3! = 36