In the provided image, we have two intersecting lines with angle relationships. Specifically, the angles labeled $118^\circ$ and $(8x + 6)^\circ$ form a pair of vertical angles, which are always congruent (equal).

Step-by-Step Solution:

1. Set the two angles equal: Since the two angles are vertical angles, we can set them equal to each other. $118^\circ = (8x + 6)^\circ$

2. Solve for $x$: $118 = 8x + 6$ Subtract 6 from both sides: $112 = 8x$ Divide both sides by 8: $x = \frac{112}{8} = 14$

So, $x = 14$.

Would you like any further details or have any questions?

Further Questions to Consider:

1. What property do vertical angles have?
2. How can we use angle relationships in parallel lines to find unknown angles?
3. Can you find other angles in the diagram based on the value of $x$?
4. What would happen if you were given supplementary angles instead of vertical angles?
5. How would you solve for $x$ if the angle given was a right angle?

Tip: Always look for congruent or supplementary angles in diagrams to set up your equations efficiently.