To solve the problem and write down the smallest 4-digit even number using the cards 7, 8, 4, and 9, where each digit is used only once:

Steps:

1. The number must be even, meaning the last digit must be one of the even numbers available, which are 8 or 4.
2. To make the smallest number, we should use the smaller even number as the last digit. So, the last digit should be 4.
3. For the first three digits, we want to place the remaining numbers in ascending order to create the smallest possible number.

The remaining digits are 7, 8, and 9. Arranging these in ascending order gives 789.

Conclusion:

The smallest 4-digit even number is 7894.

Would you like further details or have any questions? Here are some additional related questions to explore:

1. What would be the largest 4-digit even number using the same cards?
2. What is the smallest odd number that can be made from the cards?
3. How many different 4-digit numbers can be made from these four cards?
4. What is the sum of the digits in the smallest even number?
5. How would the solution change if all four digits had to be odd?

Tip: When trying to create the smallest or largest numbers, always prioritize digit placement by significance—smallest numbers should have the smallest digits in higher places, and largest numbers should have the largest digits.