Let's solve the equation \( 2(3y - 1) - 4(y + 5) = -6 \) step by step.

### Step 1: Distribute the constants
Distribute the \(2\) across \((3y - 1)\) and the \(-4\) across \((y + 5)\):

\[
2(3y - 1) = 6y - 2
\]
\[
-4(y + 5) = -4y - 20
\]

Now, the equation becomes:

\[
6y - 2 - 4y - 20 = -6
\]

### Step 2: Combine like terms on the left-hand side
Combine the \(y\) terms and the constant terms:

\[
(6y - 4y) + (-2 - 20) = -6
\]
\[
2y - 22 = -6
\]

### Step 3: Solve for \(y\)
Add 22 to both sides of the equation to isolate the term with \(y\):

\[
2y - 22 + 22 = -6 + 22
\]
\[
2y = 16
\]

Now, divide both sides by 2 to solve for \(y\):

\[
y = \frac{16}{2}
\]
\[
y = 8
\]

### Final Answer:
\[
y = 8
\]

Would you like further explanation or have any questions?

Here are some related questions:
1. How do you handle solving equations with multiple distribution steps?
2. How can you check your solution for correctness in a linear equation?
3. What is the elimination method in solving systems of equations?
4. How do linear equations differ from quadratic equations?
5. How can you solve inequalities using similar steps to solving equations?

**Tip:** When distributing negative signs, be careful to distribute to all terms within the parentheses.

Learn how to solve the equation 2(3y - 1) - 4(y + 5) = -6 with a detailed step-by-step solution. This problem covers algebraic concepts such as equations, distributive property, combining like terms, and solving linear equations. Suitable for students in Grades 7-9.

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