Concept: Its a question testing basics from the concepts of Unit Digit

Solution:
 
In ((36472)^123!) ,the last two digits of 123! would be 00 as it is a factorial and hence we can say that it is divisible by 4.The unit digit depends on the unit digit of 2^(123!)

Cyclicity of 2 is 4 and hence the unit digit for ((36472)^123!) would be 6 (2^1=2; 2^2 = 4; 2^3 = 8 and 2^4=..6 )

In ((34767)^76!),the last two digits of 76! would be 00 and hence divisible by 4.The unit digit depends on the unit digit of 7^(76!)

Cyclicity of 7 is 4 and hence the unit digit for ((34767)^76!) would be 1 (7!=7 ; 7^2=..9 ; 7^3=..3 ;7^4=..1)

Hence the Unit digit in the expression ((36472)^123!)((34767)^76!)

= 6 x 1 = 6 (option e)