The image shows a multiple-choice question asking for the inverse function of $g(x) = 6^{(x + 8)}$.

To find the inverse of a function like this, follow these steps:

Steps to find the inverse:

1. Write the equation for $g(x)$: $g(x) = 6^{(x + 8)}$

2. Replace $g(x)$ with $y$: $y = 6^{(x + 8)}$

3. Solve for $x$ in terms of $y$: To do this, take the logarithm (base 6) of both sides: $\log_6(y) = x + 8$

4. Solve for $x$: $x = \log_6(y) - 8$

5. Replace $y$ with $x$ to get the inverse function: $g^{-1}(x) = \log_6(x) - 8$

Conclusion:

The correct inverse function is: $g^{-1}(x) = \log_6(x) - 8$

Looking at your options, the second one matches this result: $g^{-1}(x) = \log_6(x) - 8$

Do you need any further clarifications or details?

Here are 5 related questions you might find interesting:

1. How do we handle logarithms with different bases when solving for an inverse?
2. How can I verify if two functions are indeed inverses of each other?
3. What happens to the domain and range when you find the inverse of a function?
4. How do exponential functions behave when reversed by logarithms?
5. Can inverse functions always be represented in a closed form?

Tip: When working with logarithmic functions, remember the basic property: $\log_b(a) = c$ means $b^c = a$.