What is the value of x so that the seven digit number 6913 x 08 is divisible by 88?

Given that,

6913 x 08

The given number will be divisible by 88 if it will be individually divisible by 11 and 8.

Divisibility of 8: 

Any number is divisible by 8 if the last three digits of that number will be divisible by 8.

the minimum possible value for which it is divisible by 8 is x=0,2,4,6,8

Divisibility by 11:

A number is divisible by 11 if we subtract and then add the digits in an alternate pattern from left to right, if it is either 0 or 11, then it will be divisible by 11 otherwise not.

$$\Rightarrow 6913 x 08$$

$$\Rightarrow (8+x+1+6) - (0+3+9)=15-12+x=3+x $$

There is only one value for which both are satisfying the condition, which is x=8.

Hence, the number will be 6913808.
Hence, the minimum value of x should be 8.