If the 7-digit number 2y6810x is divisible by 88, then what is the value of the product of x and y?

A number is divisible by 88 if it is divisible by both 8 and 11.
Divisibility by 8:
The last three digits of the number (10x) must be divisible by 8.
Testing possible values for the single digit x:

If x=4, 104÷8=13 (perfectly divisible).
Thus, x=4.

The number becomes 2y68104.

Divisibility by 11:
Sum of digits at odd positions: 2+6+1+4=13
Sum of digits at even positions: y+8+0=y+8

The difference must be a multiple of 11 or 0:

13−(y+8)=5−y
For this to equal 0, y must be 5.

Now, we calculate the product of x and y:

Product=x×y=4×5=20