To solve the equation $3x - 6 = 5x + 6$, we can follow these steps:

1. Move all terms involving $x$ to one side of the equation and constant terms to the other side.
   Subtract $3x$ from both sides to get: $-6 = 5x - 3x + 6$

2. Simplify the equation.
   Combine like terms: $-6 = 2x + 6$

3. Isolate the $x$ term.
   Subtract 6 from both sides: $-6 - 6 = 2x$ $-12 = 2x$

4. Solve for $x$.
   Divide both sides by 2: $x = -6$

The solution to the equation is $x = -6$.

Would you like more details or have any questions?

Here are five related questions to consider:

1. How do you check if $x = -6$ is the correct solution for the equation?
2. What happens if you move $5x$ to the left side of the equation instead?
3. How would the solution change if the equation were $3x - 6 = 5x - 6$?
4. What if the equation had more variables or more complex terms?
5. How can you graphically represent this equation and its solution?

Tip: Always double-check your solution by substituting it back into the original equation to verify that both sides are equal.