1. **State the problem:** Tina has the data set $\{x, 3, 3, 4, 6\}$. We know the median of this data is 4. We need to find which value of $x$ (either 3 or 6) makes the median 4. 2. **Recall the median definition:** The median is the middle value when the data is arranged in ascending order. 3. **Arrange the data and find the median:** Since there are 5 numbers, the median is the 3rd number in the sorted list. 4. **Test $x=3$:** Sorted data: $\{3, 3, 3, 4, 6\}$ The 3rd number is 3, so median would be 3, not 4. 5. **Test $x=6$:** Sorted data: $\{3, 3, 4, 6, 6\}$ The 3rd number is 4, so median is 4. 6. **Conclusion:** The value of $x$ must be 6 to have a median of 4. **Final answer:** $x=6$