Let's solve the expression step by step.

### Expression:
\[
-3 \times \left[ 4 \times (3 - 2) - (-5 + 16) + 12 \right] - 16
\]

#### Step 1: Simplify inside the parentheses
1. **Inside the first set of parentheses:**
   \[
   3 - 2 = 1
   \]
   So the expression becomes:
   \[
   -3 \times \left[ 4 \times 1 - (-5 + 16) + 12 \right] - 16
   \]

2. **Simplify inside the next set of parentheses:**
   \[
   -5 + 16 = 11
   \]
   So the expression becomes:
   \[
   -3 \times \left[ 4 \times 1 - 11 + 12 \right] - 16
   \]

#### Step 2: Simplify the multiplication and addition/subtraction inside the brackets
1. **Multiply:**
   \[
   4 \times 1 = 4
   \]
   Now the expression is:
   \[
   -3 \times \left[ 4 - 11 + 12 \right] - 16
   \]

2. **Perform the addition and subtraction:**
   \[
   4 - 11 = -7
   \]
   \[
   -7 + 12 = 5
   \]
   So the expression becomes:
   \[
   -3 \times 5 - 16
   \]

#### Step 3: Perform the multiplication and subtraction
1. **Multiply:**
   \[
   -3 \times 5 = -15
   \]

2. **Subtract:**
   \[
   -15 - 16 = -31
   \]

### Final Answer:
\[
\boxed{-31}
\]

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

1. How would the result change if the initial multiplier were positive instead of negative?
2. What happens if you change one of the numbers inside the parentheses?
3. How does the order of operations affect the final result?
4. Can you express the same problem using different mathematical notations?
5. What if the subtraction at the end was replaced by addition?

**Tip:** Always remember to follow the order of operations (PEMDAS/BODMAS) when solving expressions.

Learn how to simplify the expression -3 * [4*(3-2) - (-5+16) + 12] - 16 step-by-step. This problem covers key algebraic concepts, including order of operations (PEMDAS) and basic arithmetic. Suitable for students in Grades 6-8.

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