We have to find the unit digit only.
In 267 unit digit is 7 and cyclicity of 7 is 4.
So, (267)153 can be written as (267)Rem(153)/4 = (267)1
Unit digit of (267)1 = 7.
similarly for 66666 unit digit is 6 and cyclicity for 6 is 1.
Unit digit for (66666)72 = 6.
Therefore , Unit digit of the resultant is 7 * 6 = 2
