Permutations and combinations

the sum of all 4 digit number containing the digits 2,4,6 & 8 = 133,320

how to get it you can write all possible combination (24 combinations) and sum them

or 

use math

total combinations = 4 x 3 x 2 x 1 = 24

if you add the ones digit you will get 120, because the you have 6 numbers ending with 8, 6 ending with 6, 6 ending with 4 and 6 ending with 2

same with the ten-digit, hundred and thousand

so once digit = 0 and carry 12 to tens digit
ten digit = 120+ 12 = 132; = 2 carry 13
hundred = 120 + 13 = 133 = 3 carry 13
and thousand = 120 + 13 = 133

you have 133,320

The solution given by sanket is absolutely correct. But there is a easier way of arriving at it. total  no. of appearances of a number in each digit's place is 24/4 = 6. now sum of digits is 2+4+6+8 = 20. so total sum in each place is 6*20 = 120. now in each digits place the sum is 120 so we have to add 1111 120 times. so answer is 120*1111 = 1,33,320