Here we use the counting principle. We consider the number of possibilities for each digit and multiply them.
Let’s think about the first digit. We are told it must be 9 so there is only 1 choice for the first digit.
Let’s consider the last digit. Since the number is even the last digit must be even so it must be 0,2,4,6 or 8. That’s 5 choices.
Now there are 10 numbers we can use : 0,1,2,3,4,5,6,7,8,9 and we have used 2 of them. That leaves 8 and since the digits can’t repeat there are 8 ways to pick the second digit, and 7 ways to pick the third...keep this up and we have 6 ways to pick the fourth, 5 ways to pick the fifth, 4 ways to pick the sixth and so on. Remember there’s five ways to pick the last digit.
That means there are: (1)(8)(7)(6)(5)(4)(3)(2)(1)(5) possible account numbers. Multiplying yields: 201,600 possible account numbers.
