Since a 4-digit number cannot begin with 0, we must consider two cases:
- 4-digit numbers with 0 in the units position
- 4-digit numbers with 2, 4 or 6 in the units position

4-digit numbers with 0 in the units position
We can choose a digit for the units position in 1 way (since the units digit must be 0)
We can choose a digit for the tens position in 6 ways (since are 6 digits remaining to choose from)
We can choose a digit for the hundreds position in 5 ways (we can choose any of the 5 remaining digits)
We can choose a digit for the thousands position in 4 ways (we can choose any of the 4 remaining digits)
By the Fundamental Counting Principle (FCP), we can complete all 4 steps (and thus create a 5-digit number) in (1)(6)(5)(4) ways (= 120 ways)

4-digit numbers with 2, 4 or 6 in the units position
We can choose a digit for the units position in 3 ways (since the units digit can be 2, 4 or 6)
We can choose a digit for the THOUSANDS position in 5 ways (since are 5 NON-ZERO digits remaining to choose from)
We can choose a digit for the tens position in 5 ways (we can choose any of the 5 remaining digits)
We can choose a digit for the hundreds position in 4 ways
By the Fundamental Counting Principle (FCP), we can complete all 4 steps (and thus create a 5-digit number) in (3)(5)(5)(4) ways (= 300 ways)

So, the total number of four digit numbers possible = 120 + 300 = 420

Answer: A