The equation you need to solve is:

$6 = 8 + |9x - 4|$

Step-by-step solution:

1. Isolate the absolute value:

$6 - 8 = |9x - 4|$ $-2 = |9x - 4|$

2. Analyze the result:

An absolute value $|A|$ is always non-negative, meaning it cannot be a negative number. Here, we have $|9x - 4| = -2$, which is impossible.

Conclusion:

There is no solution to this equation because an absolute value cannot be negative.

Thus, the solution set is the empty set: $\emptyset$.

Let me know if you need more details, and feel free to ask any of the following questions for further practice:

1. How do you solve equations involving absolute values?
2. Can you explain cases when an absolute value equation has no solution?
3. What is the general method for solving $|Ax + B| = C$?
4. How do you graph absolute value equations?
5. Can absolute values ever be negative?

Tip: Always check if the absolute value equation results in a negative value. If it does, there's no solution!