Let's walk through the solution to this problem step-by-step:
1. First, simplify the expression inside the first set of curly braces:
[tex]\[
-\{10 + (-8 - 4 + 2) + 3[10 / (-6 + 4) - 9] \times 2\}
\][/tex]
2. Simplify the expression inside the inner parentheses:
[tex]\[
-8 - 4 + 2 = -10
\][/tex]
Now the expression becomes:
[tex]\[
-\{10 + (-10) + 3[10 / (-6 + 4) - 9] \times 2\}
\][/tex]
3. Simplify the expression inside the first bracket:
[tex]\[
-6 + 4 = -2
\][/tex]
So the expression is now:
[tex]\[
-\{10 + (-10) + 3[10 / -2 - 9] \times 2\}
\][/tex]
4. Perform the division inside the bracket:
[tex]\[
10 / -2 = -5
\][/tex]
Now the expression becomes:
[tex]\[
-\{10 + (-10) + 3[-5 - 9] \times 2\}
\][/tex]
5. Simplify the expression inside the bracket involving subtraction:
[tex]\[
-5 - 9 = -14
\][/tex]
Now the expression is:
[tex]\[
-\{10 + (-10) + 3[-14] \times 2\}
\][/tex]
6. Multiply inside the bracket:
[tex]\[
3 \times -14 = -42
\][/tex]
The expression now becomes:
[tex]\[
-\{10 + (-10) - 42 \times 2\}
\][/tex]
7. Perform the multiplication involving 42:
[tex]\[
-42 \times 2 = -84
\][/tex]
Now the expression is:
[tex]\[
-\{10 + (-10) - 84\}
\][/tex]
8. Simplify inside the curly braces:
[tex]\[
10 + (-10) = 0
\][/tex]
So we have:
[tex]\[
-\{0 - 84\}
\][/tex]
9. Simplify the entire expression inside the curly braces:
[tex]\[
0 - 84 = -84
\][/tex]
Therefore, we have:
[tex]\[
-(-84)
\][/tex]
Which simplifies to:
[tex]\[
84
\][/tex]
10. Now, include the remaining parts of the expression:
[tex]\[
84 + 9 - 5
\][/tex]
11. Perform the addition:
[tex]\[
84 + 9 = 93
\][/tex]
12. Perform the final subtraction:
[tex]\[
93 - 5 = 88
\][/tex]
Hence, the final answer to the problem is:
[tex]\[
\boxed{88}
\][/tex]
