The even digits are {0,2,4,6,8}.
For an integer to be divisible by 5 it must either end in 0 or 5.
5 isn't an even digit, so it can only end in 0.

We can choose the last digit only 1 way, 0.
We can choose the first digit any of the 4 remaining ways: {2,4,6,8}.
We can choose the second digit 3 ways, any of the 3 remaining even 
digits that weren't chosen for the first or third digit.

That's 1×4×3 = 12.  Here they all are: 

 1. 240
 2. 260
 3. 280
 4. 420
 5. 460
 6. 480
 7. 620
 8. 640
 9. 680
10. 820
11. 840
12. 860

Edwin