To solve for $x$ in the given problem, we need to use the fact that the lines $l$ and $m$ are parallel. When two parallel lines are intersected by a transversal, the corresponding angles are equal.

Here, the corresponding angles are $x + 6$ and $2x - 36$.

So, we set them equal to each other:

$x + 6 = 2x - 36$

Now, solve for $x$:

1. Subtract $x$ from both sides:

$6 = x - 36$

2. Add 36 to both sides:

$42 = x$

So, the value of $x$ is $\boxed{42}$.

Would you like more details or have any questions?

Here are some related questions to explore:

1. What are corresponding angles in the context of parallel lines and a transversal?
2. Can we use alternate interior angles to solve a similar problem? How?
3. What other angle relationships exist when two parallel lines are intersected by a transversal?
4. How would the solution change if the angles given were alternate exterior angles?
5. What are some real-world applications of parallel lines and transversals?

Tip: Always check if angles are corresponding, alternate interior, or alternate exterior when dealing with parallel lines and a transversal—they provide key clues to solving for unknown variables.