Choose the most restrictive digit first.

Since the number must be even, and can't end with 0,
it must end with either 2 or 6.

So we can choose the last digit 2 ways.

Choose the next most restrictive digit next.
The first digit cannot be 0 or the digit we chose for 
the last digit. 

So we can choose the first digit any of 4 ways.

We can choose the second digit any of the 4 digits we
haven't already chosen for the last and first digits.

So we can choose the 2nd digit 4 ways.

We can choose the third digit any of the 3 digits we
haven't already chosen for the last, first, and 
second digits.

So we can choose the 3rd digit 3 ways.

That's 2*4*4*3 or 96 ways.

Here they all are, 8 rows of 12 each, computer generated:

1026, 1052, 1056, 1062, 1092, 1096, 1206, 1256, 1296, 1502, 1506, 1526,
1562, 1592, 1596, 1602, 1652, 1692, 1902, 1906, 1926, 1952, 1956, 1962,
2016, 2056, 2096, 2106, 2156, 2196, 2506, 2516, 2596, 2906, 2916, 2956,
5012, 5016, 5026, 5062, 5092, 5096, 5102, 5106, 5126, 5162, 5192, 5196,
5206, 5216, 5296, 5602, 5612, 5692, 5902, 5906, 5912, 5916, 5926, 5962,
6012, 6052, 6092, 6102, 6152, 6192, 6502, 6512, 6592, 6902, 6912, 6952,
9012, 9016, 9026, 9052, 9056, 9062, 9102, 9106, 9126, 9152, 9156, 9162,
9206, 9216, 9256, 9502, 9506, 9512, 9516, 9526, 9562, 9602, 9612, 9652.

Edwin