Okay, let's think through this step-by-step:
* We are looking for 4-digit numbers using only the digits 4 and 6
* There are 4 positions to fill in a 4-digit number
* For the first position, we have 2 choices - either 4 or 6
* For the second position, we again have 2 choices - 4 or 6
* Similarly, for the third and fourth positions, we have 2 choices each
* So for each position, we have 2 choices. And we need to fill 4 positions.
* Using the fundamental principle of counting, the total number of 4-digit numbers we can make is:
* Number of choices for first position * Number of choices for second position * Number of choices for third position * Number of choices for fourth position
* Which is: 2 * 2 * 2 * 2 = 16
Therefore, the total number of 4-digit numbers that can be written using only the digits 4 and 6 is 16.