Let's solve the equation step by step:

The given equation is:
\[
-4(y - 2) + 6(3y + 1) = 10
\]

### Step 1: Distribute the constants.
Distribute \(-4\) and \(6\) across the terms inside the parentheses:

\[
-4(y - 2) = -4y + 8
\]
\[
6(3y + 1) = 18y + 6
\]

So, the equation becomes:
\[
-4y + 8 + 18y + 6 = 10
\]

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

\[
(-4y + 18y) + (8 + 6) = 10
\]
\[
14y + 14 = 10
\]

### Step 3: Isolate the variable \(y\).
Subtract 14 from both sides to move the constant term to the right side:

\[
14y = 10 - 14
\]
\[
14y = -4
\]

### Step 4: Solve for \(y\).
Divide both sides by 14:

\[
y = \frac{-4}{14}
\]
\[
y = -\frac{2}{7}
\]

So, the solution is:
\[
\boxed{y = -\frac{2}{7}}
\]

Would you like more details or have any questions?

### Relative Questions:
1. How do you distribute coefficients when solving linear equations?
2. What are like terms, and how do you combine them?
3. Why do we subtract or add terms on both sides of an equation when solving for a variable?
4. How can we check if our solution for \(y\) is correct?
5. How would the solution change if the constants on the right-hand side of the equation were different?

**Tip:** Always check your final answer by substituting it back into the original equation to ensure it satisfies the equation.

Learn how to solve the equation -4(y - 2) + 6(3y + 1) = 10 with a detailed step-by-step solution. This problem covers key algebraic concepts, including equations, distributive property, combining like terms, and isolating variables. Suitable for students in Grades 7-9.

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