We have four choices for the tens digit and three choices for the units digit,
so there are a total of $4 \times 3 = \boxed{12}$ distinct two-digit positive integers that can be created.
The answer is: 12
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Using the digits 2, 4, 6, and 7, how many distinct two-digit positive integers can be created if each digit can only be used once?

### Answer:
