Explanation:

To form a four-digit number that is divisible by 4 using the given numbers 2, 3, 6, and 7, we need to consider the divisibility rules for 4.

Divisibility Rule for 4:
A number is divisible by 4 if the last two digits of the number are divisible by 4.

Step 1:
We need to consider all the possible combinations of the given numbers to form a four-digit number.

Step 2:
Examine each combination to check if the last two digits are divisible by 4.

Step 3:
Count the number of combinations that satisfy the divisibility rule for 4.

Combinations:
Using the given numbers 2, 3, 6, and 7, we can form the following combinations:

- 2367
- 2376
- 2637
- 2673
- 2763
- 2736
- 3267
- 3276
- 3627
- 3672
- 3726
- 3762
- 6237
- 6273
- 6327
- 6372
- 6723
- 6732
- 7236
- 7263
- 7326
- 7362
- 7623
- 7632

Checking Divisibility:
Now, we need to check if the last two digits of each combination are divisible by 4.

- 2367: Not divisible by 4
- 2376: Divisible by 4
- 2637: Not divisible by 4
- 2673: Divisible by 4
- 2763: Divisible by 4
- 2736: Divisible by 4
- 3267: Not divisible by 4
- 3276: Divisible by 4
- 3627: Not divisible by 4
- 3672: Divisible by 4
- 3726: Divisible by 4
- 3762: Divisible by 4
- 6237: Not divisible by 4
- 6273: Divisible by 4
- 6327: Not divisible by 4
- 6372: Divisible by 4
- 6723: Not divisible by 4
- 6732: Not divisible by 4
- 7236: Divisible by 4
- 7263: Divisible by 4
- 7326: Divisible by 4
- 7362: Divisible by 4
- 7623: Not divisible by 4
- 7632: Not divisible by 4

Counting Divisible Combinations:
Out of the 24 combinations, 8 of them satisfy the divisibility rule for 4.

Therefore, the correct answer is '8'.