Let's simplify the given expression:

[ [2 + \sqrt{4 - x}] - [2 - \sqrt{4 - x}] ]

Step 1: Distribute the negative sign

We distribute the negative sign to the second bracket:

$2 + \sqrt{4 - x} - 2 + \sqrt{4 - x}$

Step 2: Combine like terms

The $2$ and $-2$ cancel each other out, so we are left with:

$\sqrt{4 - x} + \sqrt{4 - x}$

Step 3: Simplify further

We can now combine the two square roots:

$2\sqrt{4 - x}$

Thus, the simplified expression is:

$2\sqrt{4 - x}$

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Would you like more details or have any further questions on this? Here are some related questions:

1. How do you simplify expressions involving square roots?
2. What is the domain of the expression $\sqrt{4 - x}$?
3. How do you solve for $x$ in an equation involving square roots?
4. What happens when you square both sides of an equation with square roots?
5. Can you apply this method to more complex algebraic expressions?

Tip: When simplifying square roots, always be mindful of their domain—ensure the expression inside the root is non-negative (i.e., no square roots of negative numbers).