Let's solve the equation step by step:

The given equation is:

$2(y - 6) = 3(y - 4) - y$

Step 1: Expand both sides of the equation

On the left-hand side, expand the expression: $2(y - 6) = 2y - 12$

On the right-hand side, expand the expression: $3(y - 4) - y = 3y - 12 - y$

Now the equation looks like: $2y - 12 = 3y - 12 - y$

Step 2: Combine like terms

On the right-hand side, combine the $3y$ and $-y$: $2y - 12 = 2y - 12$

Step 3: Subtract $2y$ from both sides

$2y - 12 - 2y = 2y - 12 - 2y$

This simplifies to: $-12 = -12$

Step 4: Interpret the result

The equation $-12 = -12$ is always true, which means this equation is an identity. Therefore, the solution is all real numbers.

Final Answer:

The equation holds true for all values of $y$. Hence, the solution is: $y \in \mathbb{R}$

Would you like further clarification on any step or additional details?

Follow-up Questions:

1. What is an identity equation, and how is it different from a contradiction?
2. How do you solve equations with no solution, known as contradictions?
3. What happens if you have a quadratic equation instead of a linear one?
4. How do you deal with absolute value in equations like this?
5. Can you solve an equation that includes fractions on both sides?

Tip:

Always remember to simplify both sides of an equation fully before attempting to move terms around. This avoids mistakes and makes solving easier.