https://file.aiquickdraw.com/mathbot/file/1726469796859skdyok2y.jpg

The equation in the image is:

\[
3 \times (2y - 4) = -2 \times (3y + 2)
\]

### Step-by-Step Solution:

1. **Distribute** the numbers outside the parentheses:
   \[
   3 \times (2y - 4) = 6y - 12
   \]
   \[
   -2 \times (3y + 2) = -6y - 4
   \]

   Now the equation becomes:
   \[
   6y - 12 = -6y - 4
   \]

2. **Move all terms involving** \( y \) to one side of the equation. Add \( 6y \) to both sides:
   \[
   6y + 6y - 12 = -4
   \]
   \[
   12y - 12 = -4
   \]

3. **Isolate the term** with \( y \) by adding 12 to both sides:
   \[
   12y = 8
   \]

4. **Solve for** \( y \) by dividing both sides by 12:
   \[
   y = \frac{8}{12} = \frac{2}{3}
   \]

So, the solution is:
\[
y = \frac{2}{3}
\]

Would you like more details on any step, or do you have any questions?

### Related Questions:
1. How do you solve equations with parentheses and distribution?
2. What happens when variables appear on both sides of an equation?
3. How can you check if your solution to an equation is correct?
4. How do you solve equations with fractions?
5. How do you handle negative signs when distributing in an equation?

**Tip:** Always simplify both sides of the equation as much as possible before moving terms around.

Solve the equation: 3 × (2y - 4) = -2 × (3y + 2)

This detailed solution shows how to solve the linear equation 3(2y - 4) = -2(3y + 2) using the distributive property and balancing both sides of the equation. Suitable for students in Grades 8-10, this problem covers key algebra concepts.

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