Answer: Instead of stars 8, 6 digits should go in 517** respectively to make the 5 digit number which is a multiple of 6, 7, and 9.
Explanation:
Conditions for stars places:
1. Ones place should be even the number being divisible by 6.
2. The sum of ones and tens face value should be either 5 or 14 for the number to be divisible by 9.
Case 1: when the sum of ones and tens face values are 5.
So, we have three numbers that match the required condition:
51732, 51750, and 51714
But all of the numbers are not divisible by 7.
Case 2. When the sum of ones and tens face values are 14.
So, we have two numbers that match the required condition:
51786 and 51768
The number 51786 is divisible by 7.