Let's solve the equation step by step:

Given:  
\[ 6(2 - y) + 7y = 2y \]

### Step 1: Distribute the 6 on the left-hand side.
\[
6 \times 2 - 6 \times y + 7y = 2y
\]
\[
12 - 6y + 7y = 2y
\]

### Step 2: Combine like terms on the left-hand side.
\[
12 + (7y - 6y) = 2y
\]
\[
12 + y = 2y
\]

### Step 3: Move the \( y \) term to one side by subtracting \( y \) from both sides.
\[
12 = 2y - y
\]
\[
12 = y
\]

### Final Answer:
\[
y = 12
\]

Would you like further details or clarifications on any steps?

Here are 5 related questions for further exploration:
1. What if the equation were \( 6(2 - y) + 7y = 3y \)?
2. How would you solve \( 5(3 - y) + 8y = 4y \)?
3. What happens when the equation is \( 7(1 - y) + 6y = y \)?
4. How do you solve a quadratic equation like \( 2y^2 + 3y - 5 = 0 \)?
5. Can you solve a system of equations involving \( y \) and \( x \)?

**Tip:** When solving equations, always simplify by combining like terms and isolating the variable step by step!

Learn how to solve the linear equation 6(2 - y) + 7y = 2y with a step-by-step breakdown. This problem involves key algebraic concepts like the distributive property and combining like terms, suitable for students in Grades 6-8.

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