If 5432*7 is divisible by 9 then the digit in place of * is

Divide as far out as possible ^ shown in picture

When you get to 5*, you have to assume that the * holds the place of a number that will make 5* indivisible by 9 because 7 is indivisible by 9.

The only case when a number with the second digit being 7 is divisible by 9 is when it is a 2, so it can be assumed that the number remaining will look like 5* - a given number must be 2....

The next step is to look at the multiplicative possible answers of the 9s table - 9x6 for example is 54... the only number within those restrictions that is in the 50s and could possibly give an answer like 2... other numbers will result in an answer that is too big.

5* - 54 = 2... so
* will hold the digit 6

6 is the answer