The digits are 1,2,3,4,5,6,7,8,9,and 0

The even ones are 0,2,4,6,8.  The odd ones are 1,3,5,7,9

Let's try the even digit 0.

0×0 = 0.  There is only one digit, so that can't be it.

Let's try the even digit 2.

2×2 = 4.  There is only one digit, so that can't be it either.

Let's try the even digit 8.

8×8 = 64.  Let's find the sum of the digits 6+4=10.  No, 10 is not 9,
so it's not 8

I skipped the even digit 6, didn't I?  

Let's try the even digit 6

6×6 = 36 and the sum of its digits is 3+6 or 9.

What do you know?  That must be the answer, 6.

Now was that really too difficult for you to answer all by yourself?

Edwin