If the six-digit number 6x2904 is divisible by 88, then the value of x is:

To find the value of x, we need to understand that a number is divisible by 88 if and only if it is divisible by both 8 and 11 (since 88 is a product of 8 and 11).

1. For a number to be divisible by 8, the last three digits must form a number that is divisible by 8. In this case, the last three digits are x04. The only values of x that make x04 divisible by 8 are 0, 1, 2, and 3.

2. For a number to be divisible by 11, the difference between the sum of the digits at the odd positions and the sum of the digits at the even positions must be divisible by 11. In this case, the sum of the digits at the odd positions is 6+x+0 = 6+x, and the sum of the digits at the even positions is 2+9+4 = 15. Therefore, the difference is (6+x) - 15 = x - 9.

3. The only values of x that make x - 9 divisible by 11 are 9 and 20. However, x must be a single digit, so x = 9 is the only possible value.

Therefore, the value of x is 9.