Solve : `[{12-(15-:3-2)}+6]-4`

Answer

To solve the expression `[{12-(15-:3-2)}+6]-4`, we will follow the order of operations (also known as BODMAS/BIDMAS rules: Brackets, Orders, Division and Multiplication, Addition and Subtraction).

### Step-by-Step Solution:

1. **Identify the innermost bracket**: We start with the expression inside the brackets: `(15-:3-2)`.
- Here, `15-:3` means `15 divided by 3`.

**Hint**: Always start solving from the innermost brackets.

2. **Perform the division**: Calculate `15 ÷ 3`.
- \( 15 ÷ 3 = 5 \)

**Hint**: Remember that division comes before subtraction in the order of operations.

3. **Substitute the result back**: Now replace `15-:3` with `5` in the expression.
- The expression now looks like: `12 - (5 - 2)`.

**Hint**: Always keep track of your substitutions to avoid confusion.

4. **Perform the subtraction inside the brackets**: Now calculate `5 - 2`.
- \( 5 - 2 = 3 \)

**Hint**: Solve the operations inside the brackets first before moving outside.

5. **Substitute the result back**: Replace `(5 - 2)` with `3` in the expression.
- The expression now looks like: `12 - 3 + 6 - 4`.

**Hint**: Keep simplifying step by step.

6. **Perform the subtraction**: Now calculate `12 - 3`.
- \( 12 - 3 = 9 \)

**Hint**: Always perform operations from left to right when there are no brackets.

7. **Add 6**: Now add `6` to `9`.
- \( 9 + 6 = 15 \)

**Hint**: Addition is straightforward; just combine the numbers.

8. **Subtract 4**: Finally, subtract `4` from `15`.
- \( 15 - 4 = 11 \)

**Hint**: The last step is simply to subtract the last number.

### Final Answer:
The final result of the expression `[{12-(15-:3-2)}+6]-4` is **11**.