If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions...

1. Translate the problem requirements: We need to find how many different four-digit telephone extensions can be formed using digits 1, 2, 3, and 6 exactly once, subject to the extension being even.
2. Identify the constraint: Only 2 or 6 can occupy the last digit to yield an even number.
3. Fix the constrained position: Place 2 or 6 last, then permute the remaining three digits (\(3! = 6\) ways each).
4. Apply the multiplication principle: Sum the cases to get 12 total extensions.

Execution

Case 1: Ends in 2 → \(3! = 6\) ways. Case 2: Ends in 6 → \(3! = 6\) ways. Total = 12.

Final Answer

12