We must choose the first digit as 4,5 or 6, but since the
last digit must be 2,4, or 6 it will be a different number
of even numbers if we choose 5 for the first digit than if
we choose 4 or 6 for it. So we consider three cases.
Case 1. We choose 4 for the first digit.
We choose the last digit any of 2 ways. (2 or 6)
We choose the middle digit any of the remaining 4 ways.
That's 1 = 8 ways.
Case 2. We choose 5 for the first digit.
We choose the last digit any of 3 ways, {2,4, or 6}
We choose the middle digit any of the remaining 4 ways.
That's 1 = 12 ways.
Case 3. We choose 6 for the first digit. That's the same as case 1,
So that's also 8 ways.
Answer: 8+12+8 = 28 ways.
Here are all 28 ways,
412 416 426 452 456 462 492
496 512 514 516 524 526 542
546 562 564 592 594 596 612
614 624 642 652 654 692 694
Edwin