We have 6 choices for the first pair, 5 choices for the second pair, and 4 choices for the odd die. Multiply this by the number of ways to choose 2 from 6, and divide by the different outcomes, hence:
Do you understand that there is no one correct way of doing this?
I would have done as
Now I can explain reasoning. The six choose 2 is the number of ways to have two pair.
The four is the number of ways to have the odd number out.
The numbers of ways to arrange is .