What digits should be placed instead of the asterisks so that the number 454** is divisible by 2, 7, and 9?

#
Let these be the digits $a$ and $b$. For the number to be even, the digit $b$ must be even, and for the number to be divisible by 9, $a+b$ must equal 5 or 14. We get five options - 45414, 45432, 45450, 45468, 45486, - of which only 45486 is divisible by 7.

Answer

45486.