In the diagram you provided, we have angles related to a pair of intersecting lines. The equation you need to solve for $x$ is based on the angle relationships shown. It looks like you are being asked to identify which equation corresponds to the angle relationships in the diagram.

Given that one angle is $3x + 6^\circ$ and the other is $3x + 96^\circ$, we are likely dealing with supplementary angles, which add up to $180^\circ$ since they are on a straight line.

The equation for supplementary angles would be:

$(3x + 6) + (3x + 96) = 180$

Simplifying this:

$6x + 102 = 180$

Subtract 102 from both sides:

$6x = 78$

Now, divide both sides by 6:

$x = 13$

Looking at the options provided, the equation that fits is:

$3x + 96 = 111$

So, the correct answer is $3x + 96 = 111$.

Let me know if you need further details or explanation. Here's a set of related questions:

1. How do you identify supplementary angles in diagrams?
2. What are complementary angles, and how do they differ from supplementary angles?
3. What would the equation look like if the angles were complementary (adding up to $90^\circ$)?
4. How do you solve for $x$ in two-step equations like this one?
5. What would happen if the equation involved vertical angles instead of supplementary angles?

Tip: When dealing with angles that form a straight line, always remember they are supplementary and sum to 180°.