The sum of all four-digit numbers that can be formed by using the digits 2, 4, 6, 8 (when repetition of digits is not allowed) is

Total numbers ending with 2 is 3! as after fixing 2 in the unit's place, other three places can be filled by 3! ways. Thus, 2 appears in the unit's place 3 ! times. Similarly, all other digits 4, 6, and 8 also appear 3 ! times. Then sum of the digits in the unit's place is 6(2 + 4 + 6 + 8) = 120. 

Similarly, sum of digits in ten's place is 120 tens and that in hundred's place is 120 hundreds, etc. Hence, sum of all the 24 numbers is  120(1 + 10+ 100+ 1000) = 120$\times$1111 = 133320