How many 4-digit even numbers have all 4 digits distinct?

A 4-digit even number must have an even digit in the units place and cannot have 0 in the thousands place. Count in two cases.
Case 1: units digit is 0. The thousands place has 9 choices (1 to 9), then the hundreds and tens places have 8 and 7 choices. Count = 9 × 8 × 7 = 504.
Case 2: units digit is one of 2, 4, 6, 8. There are 4 choices for the units place. The thousands place cannot be 0 or the chosen units digit, so it has 8 choices. The remaining two places have 8 and 7 choices. Count = 4 × 8 × 8 × 7 = 1792.
Total = 504 + 1792 = 2296. Hence, option C is correct.