The eight digit number 5x32465y is divisible by 88. What is the value of (2x + 3y) ?

Here the given number should be divisible by 88. So 88 = $$11\times8$$

A number is divisible by 8. if the last three digits of the number if divisible by 8. The last three digits of the number 5x32465y is 65y. So the only possible value of 'y' will be 6.

A number is divisible by 11. if the sum of digits on the odd places from the left end and the sum of the digit on even places from the right end difference will be zero.

(5+3+4+5) - (x+2+6+y) = 0

17 - (x+8+6) = 0

17 - x - 14 = 0

x = 17-14 = 3

Value of (2x + 3y) = $$(2\times\ 3+3\times\ 6)$$

= (6+18)

= 24