I google it and found what i think most relevent explaination without calculation

Mean = 4
Var = (16+4+0+4+16)/5 =
After addition of 2 numbers, New Var =
The question is What x will pitch New Var closest to 8 so that 56/7 = 8
OR Which of the options will give a value of x that is closest to 16
So from the 5 options find out which (deviation^2) from 4 is closest to 16
Naked eye will tell you that (A), (B) are a long shot.
(C) 1^2 + 1^2 = 2
(D) 2^2 + 2^2 = 8 ==> |16-8| = 8
(E) 4^2 + 4^2 = 32 ==> |16-32| = 16
So option (D) gives an SD that is closest to the original SD.

why such hard calculations

its simple - 0 2 4 6 8
so av appx - 4 because of even space ,
now std deviation - 4 as 8-4 = 4 & 4-0=4
now add 4 4 to each deviation will be with in the range so 4 4 should answer

try to understand the logic of ST deviation not just formula and heavy calculations