Smallest 4 positive even integer is 1000
Largest 4 digit positive even integer is 9998

Therefore total integers (9998 - 1000)/2 + 1 = 4500

Here is another method

since you want only even numbers, the last digit can be 0,2,4,6,8. Number of ways of choosing one digit out of these is 5C1 = 5

1st digit can be 1..9 (excluding 0)..so number of ways = 9C1=9

2nd digit can be 0..9..so number of ways =10C1=10
3rd digit can be 0..9..so number of ways =10C1=10

So total = 9*10*10*5 = 4500