The problem asks for the inverse of a relation. The inverse of a relation is found by switching the components of each ordered pair in the relation.

The original relation is: $\{(-2, 3), (4, 7), (3, -9), (8, 4)\}$ To find the inverse, we switch the $x$ and $y$ in each pair:

1. $(-2, 3) \rightarrow (3, -2)$
2. $(4, 7) \rightarrow (7, 4)$
3. $(3, -9) \rightarrow (-9, 3)$
4. $(8, 4) \rightarrow (4, 8)$

Thus, the inverse relation is: $\{(3, -2), (7, 4), (-9, 3), (4, 8)\}$

Looking at the answer choices, the correct inverse is the second option: $\{(3, -2), (7, 4), (-9, 3), (4, 8)\}$

Would you like more details, or do you have any other questions?

Here are 5 related questions you might find interesting:

1. How do you find the inverse of a function, rather than a relation?
2. What are some real-world examples of relations and their inverses?
3. How does a graph of a function change when you take the inverse?
4. Can all relations have inverses? If not, why?
5. What is the difference between a one-to-one function and a relation?

Tip: When finding the inverse of a function, make sure the function is one-to-one, meaning that each output is associated with exactly one input. If not, the inverse may not exist!