Given:

11- digit number = 765y88436x6 

Divisor = 72

Concept used:

First, we should have to know the factors of divisor if all the factors are divided the given number, then the number is divisibly by 72

Divisibility rule of 8: If the last three digits are divisible by then the number is divisible by 8

Divisibility of 9:  If the sum of all digits is divisible by 9 then the number is divisible by 9

2 and 4 are the factors of 8 so, if the number is divisible by 8 is also divisible by 2 and 4

3 is the factor of 9 so, if the number is divisible by 9 then the number is divisible by 3

2 and 3 are the factors of 6 

Calculations:

Factors of 72 = 1 , 2, 3, 4, 6, 8, 9

To verify the number is divisible by 8 last three digits = 6x6

If the 6x6 is divisible by 8  then the number must be 616 or 656 or 696

Hence, x = 1 or 5 or 9

To verify the number is divisible by 9 sum of digits = 7 + 6 + 5 + y + 8 + 8 + 4 + 3 + 6 + x + 6

⇒ 53 + x+ y

53 + x +y is divisible by 9 it must be either 63 

53 + x + y = 63

⇒ x + y = 63 - 53

⇒ x + y = 10 

If we substitute x = 1

1 + y = 10

⇒ y = 10 - 1

⇒ y = 9

Here, the condition is x > y so  x = 1 doesnot satisfy this condition 

If we substitute x = 5

5 + y = 10 

⇒ y = 10 -5

⇒ y = 5

x = y condition doesn't satify 

x = 9

9 + y = 10 

⇒ y = 10 - 9 

⇒ y = 1

x > y so condition satisfies

x - y = 9 - 1 

⇒ x - y = 8

∴ The required value is 8