What is the value of $2-2\{2-2[2-2(4-2)]\}$?
(a) 0
(b) 2
(c) -2
(d) 4
(e) -10
The correct option is (e).

The order of precedence for solving an expression is

$$
\underbrace{\text { parentheses }}_{1 \varrho} \rightarrow \underbrace{\text { brackets }}_{2 \varrho} \rightarrow \underbrace{\text { braces }}_{3 \propto}
$$

and

$$
\underbrace{\text { multiplications and divisions }}_{1 \varrho} \rightarrow \underbrace{\text { additions and subtractions }}_{2 \varrho}
$$

Thus,

$$
\begin{aligned}
2 & -2\{2-2[2-2(\underbrace{4-2}_{2})]\}=2-2\{2-2[2-\underbrace{2 \times 2}_{4}]\} \\
& =2-2\{2-2[\underbrace{2-4}_{-2}]\}=2-2\{2-\underbrace{2 \times(-2)}_{-4}\} \\
& =2-2\{2-(-4)\}=2-2\{\underbrace{2+4}_{6}\}=2-\underbrace{2 \times 6}_{12}=2-12=-10
\end{aligned}
$$