The function $g$ is the inverse of the function $f$. By definition, if $g$ is the inverse of $f$, then:

$g(f(x)) = x \quad \text{and} \quad f(g(x)) = x$

To find $g(2)$, we need to identify the input $x$ such that $f(x) = 2$. From the table, we can see that when $x = 4$, $f(4) = 2$.

Therefore:

$g(2) = 4$

The answer is $g(2) = 4$.

Would you like more details or have any other questions? Here are some related questions to deepen your understanding:

1. What is the inverse function concept in mathematical terms?
2. How would you find $g(-6)$ using the same table?
3. If $g$ is the inverse of $f$, how would you describe the graph of $g$ compared to $f$?
4. What are the properties of invertible functions?
5. How can we verify that a function is invertible?

Tip: Remember, the inverse of a function swaps the roles of $x$ and $y$, meaning the inputs and outputs are reversed!