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.

Learn how to solve the linear equation 2(y−6)=3(y−4)−y step-by-step, leading to an identity solution where the equation holds true for all values of y. This tutorial covers important algebraic concepts like the distributive property and identity equations, suitable for students in Grades 8-10.

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