In such problems as these, always make the most restrictive choices first.

Here the most restrictive choice is the last digit, so we choose it first.

Choose the last (or fourth) digit any of 3 ways. (either 2, 4, or 6)
Choose the first digit as any of 6 ways.
Choose the second digit as any of 6 ways.
Choose the third digit as any of 6 ways.

That's (3)(6)(6)(6) = 648 ways.

Edwin

    Choose the last (or fourth) digit any of 3 ways. (either 2, 4, or 6)

    Choose the last (or fourth) digit any of 3 ways. (either 1, 3, or 5)