Let's solve the equation step by step:

Given:
$-4(u + 2) + 2 = 2(u + 6)$

Step 1: Distribute the constants

Distribute the $-4$ on the left side and the $2$ on the right side:

$-4u - 8 + 2 = 2u + 12$

Step 2: Simplify both sides

On the left side, simplify $-8 + 2$:

$-4u - 6 = 2u + 12$

Step 3: Move the terms involving $u$ to one side

Add $4u$ to both sides to eliminate $-4u$ from the left:

$-6 = 6u + 12$

Step 4: Move the constants to the other side

Subtract $12$ from both sides to move the constant terms to one side:

$-6 - 12 = 6u$

$-18 = 6u$

Step 5: Solve for $u$

Divide both sides by 6:

$u = \frac{-18}{6}$

$u = -3$

Final Answer:

$u = -3$

Would you like more details or have any questions?

Here are 5 related questions:

1. What happens if we use the distributive property incorrectly?
2. How can we check the solution for correctness?
3. How do we solve an equation with fractions?
4. What are the different methods for solving linear equations?
5. How does moving terms from one side to another affect the equation?

Tip: Always simplify the equation step-by-step to avoid mistakes in sign handling!