We are tasked with solving the equation:

$6 - 2x = 6x - 10x + 6$

Step-by-Step Solution:

1. Simplify the right-hand side:

   The terms involving $x$ on the right side are $6x - 10x$. Simplifying this gives:

   $6x - 10x = -4x$

   So the equation becomes:

   $6 - 2x = -4x + 6$

2. Move constant terms to one side:

   Subtract 6 from both sides to eliminate the constants:

   $6 - 2x - 6 = -4x + 6 - 6$

   This simplifies to:

   $-2x = -4x$

3. Solve for $x$:

   Add $4x$ to both sides to get:

   $-2x + 4x = 0$

   Simplifying:

   $2x = 0$

   Now divide both sides by 2:

   $x = 0$

Final Answer:

The value of $x$ is 0.

Would you like further details or clarifications? Here are 5 related questions:

1. How would the solution change if the constants on both sides were different?
2. What happens if the equation had a quadratic term?
3. How do we check the solution by substituting back into the original equation?
4. Can you solve this type of equation using graphing methods?
5. How can you apply these methods to solve word problems involving linear equations?

Tip: When solving linear equations, always simplify terms on both sides before attempting to isolate the variable.