Given:

8 - digit number = 7y9745x2

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 = 5x2

If the 6x6 is divisible by 8  then the number must be 512 or 552 or 592

Hence, x = 1 or 5 or 9

To verify the number is divisible by 9 sum of digits =7 + y + 9 + 7 + 4 + 5 + x + 2

⇒ 34 + y + x

34 + y + x is divisible by 9 it must be 36 or 45 

34 + y + x = 36

⇒ x + y = 36 - 34

⇒ x + y = 2

If we substitute x = 1

1 + y = 2

⇒ y = 2 - 1

⇒ y = 1

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

Let take the  number must be 45

⇒ x + y = 45 - 34

⇒ x + y = 11

If we substitute x = 1

1 + y = 11

⇒ y = 11 - 1

⇒ y = 10

x > y  but the codition doesnt satisfy 10 is a 2 - digit number 

If we substitute x = 5

5 + y = 11

⇒ y = 11 - 5

⇒ y = 6

x < y for this condition so it doesnt satisfy

If we substitute x = 5

9 + y = 11

⇒ y = 11 - 9

⇒ y = 2

x > y so the condition satisfieed 

2x - y = 2 × 9 - 2

⇒ 18 - 2 = 16

∴ The required value is 16