Solution:

To form a four-digit number, we need to choose the thousands, hundreds, tens, and units place digits. We can choose the thousands place digit in 3 ways (2, 4, or 6). Once we choose the thousands place digit, we can choose the hundreds, tens, and units place digits in 4, 3, and 2 ways, respectively.

Total Number of Possible Outcomes: Total number of four-digit numbers that can be formed using digits 1, 2, 4, and 6 is:

3 × 4 × 3 × 2 = 72

Finding the number of outcomes that result in a number divisible by 4: A number is divisible by 4 if its last two digits are divisible by 4. So, for a four-digit number to be divisible by 4, its last two digits must be one of the following:

12, 16, 24, 26, 32, 36, 42, 46, 62, or 64.

There are 10 such combinations of the last two digits for a four-digit number formed using digits 1, 2, 4, and 6.

For each of these combinations of the last two digits, the thousands and hundreds place digits can be chosen in 3 and 4 ways, respectively, since we have used up two of the digits. The remaining digit can then be placed in one of the two remaining positions.

So, the total number of outcomes that result in a number divisible by 4 is:

10 × 3 × 4 × 2 = 240

Probability: The probability of forming a four-digit number that is divisible by 4 is:

240/72 = 10/3 or 3.33 (approx.)

Therefore, the probability of forming a four-digit number that is divisible by 4 is 10/3 or 3.33 (approx.).