Final answer:
To form two-digit numbers using the digits 5, 6, 3, and 2 without repeating any digits, there are 4 choices for the tens place and 3 remaining choices for the ones place, resulting in a total of 12 different two-digit numbers.
Step-by-step explanation:
If no digit may be used more than once, to determine how many two-digit numbers can be formed using only the digits 5, 6, 3, and 2, we need to consider the combinations possible for the tens and ones place.
For the tens place, there are 4 possible choices (5, 6, 3, or 2). Once a digit is chosen for the tens place, there are only 3 digits left to choose from for the ones place.
Therefore, the number of different two-digit numbers that can be created is found by multiplying the number of choices for the tens place by the number of choices for the ones place after the first digit is chosen.
4 choices for the tens place × 3 choices for the ones place = 12 different two-digit numbers.