Let's solve the equation $6 - 2x = 6x + 6$.

Step 1: Get all the terms involving $x$ on one side

Add $2x$ to both sides: $6 = 8x + 6$

Step 2: Isolate the $x$ term

Subtract 6 from both sides: $0 = 8x$

Step 3: Solve for $x$

Divide both sides by 8: $x = 0$

So, the solution is $x = 0$.

Would you like any further details or explanations on how this was solved? Here are some follow-up questions related to this problem:

1. What happens if we change the equation to $6 - 2x = 6x + 8$?
2. How would you solve the equation $6 - 2x = -6x + 6$?
3. What does it mean when the solution to an equation is $x = 0$?
4. How can you check if your solution to the equation is correct?
5. What is the next step if the equation had no solutions?

Tip: Always check your solution by substituting it back into the original equation to ensure it satisfies the equation.