We assume that you don't want to count numbers that start with 0, so there are 4 possible first digits and 5 possible digits in each of the remaining places.
4*5^3 = 500 . . . . total number of 4-digit numbers using only even digits
_____ The list of them would be ... 2000, 2002, 2004, 2006, 2008, 2020, ..., 8868, 8880, 8882, 8884, 8886, 8888
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