Let's simplify the expression:

$-2x + 2(4x + 2)$

1. Distribute the $2$ to both terms inside the parentheses:

$-2x + (2 \cdot 4x) + (2 \cdot 2)$

$-2x + 8x + 4$

2. Combine like terms:

$(-2x + 8x) + 4 = 6x + 4$

So, the simplified expression is:

$6x + 4$

Would you like any further details or have any questions?

Here are 5 related questions:

1. How would you solve $6x + 4 = 0$ for $x$?
2. What happens if you substitute a value for $x$ in the simplified expression?
3. Can you factor the expression $6x + 4$?
4. How does the distributive property apply to the original equation?
5. How would the solution change if the original expression were $-2x - 2(4x + 2)$?

Tip: Always check for like terms after distributing to simplify expressions quickly!