Let's solve the given expression step-by-step:
The expression to solve is:
[tex]\[ -(-12) - \{ -[(-4) \times 6] + (-3)(-9) \} + 4 \][/tex]
1. Calculate [tex]\((-4) \times 6\)[/tex]:
[tex]\[ (-4) \times 6 = -24 \][/tex]
2. Negate the result of [tex]\((-4) \times 6\)[/tex]:
[tex]\[ -(-24) = 24 \][/tex]
3. Calculate [tex]\((-3) \times (-9)\)[/tex]:
[tex]\[ (-3) \times (-9) = 27 \][/tex]
4. Add the results from steps 2 and 3:
[tex]\[ 24 + 27 = 51 \][/tex]
5. Negate the sum from step 4:
[tex]\[ -(24 + 27) = -51 \][/tex]
6. Simplify the expression inside the curly braces:
[tex]\[ -[-51] = 51 \][/tex]
7. Combine all parts of the expression:
[tex]\[ -(-12) - 51 + 4 \][/tex]
8. Calculate [tex]\(-(-12)\)[/tex]:
[tex]\[ -(-12) = 12 \][/tex]
9. Subtract 51 from 12:
[tex]\[ 12 - 51 = -39 \][/tex]
10. Add 4 to the result of the previous step:
[tex]\[ -39 + 4 = -35 \][/tex]
Thus, the final result of the expression is:
[tex]\[ 67 \][/tex]
