First, I know this was posted first here but I reposted because the answer wasn't clear for me and the question is 8 years old so it's not getting any activity.
I don't understand the reason of the split, I first solved the problem in the following way:
Last digit: we have $3$ options: $0,2,6$ since we need the number to be even.
First digit: we have $4$ options: all minus $0$ and digit picked previously
Third digit: we have $4$ options: all minus the one picked in the previous $2$ digits.
Second digit: we have $3$ options: all minus previous $3$ digits.
so we get $3*3*4*4$
However I have a logical problem here, if I start analyzing in a different order (for example last digit to first) then it seems like I am getting different result (example:last digit has $3$ options and third one has $5$, etc…)
Moreover, I don't understand the solution and why they split it into these $2$ cases.
Best Answer
If we chose $0$ as the last digit, "the digit $0$" and "the digit picked previously" are the same digit, meaning that in this case, you have $5$ options for the first digit.
This is the reason for the split.