Find the value of given expression
`(-12)[11 + {7 xx (-3)}] div [4{13 - (-3) xx (-6) }]` =
(a) -6
(b) -4
(c) 4
(d) -2

Options

A. `-6`
B. `-4`
C. 4
D. `-2`

Answer

To solve the expression `(-12)[11 + {7 × (-3)}] ÷ [4{13 - (-3) × (-6)}]`, we will follow the order of operations, often remembered by the acronym BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).

### Step-by-Step Solution:

1. **Evaluate the innermost brackets**:
- Calculate `7 × (-3)`.
\[ 7 × (-3) = -21 \]
So, the expression now looks like:
\[ (-12)[11 + (-21)] ÷ [4{13 - (-3) × (-6)}] \]

2. **Simplify the first bracket**:
- Now, calculate `11 + (-21)`.
\[ 11 - 21 = -10 \]
The expression now becomes:
\[ (-12)[-10] ÷ [4{13 - (-3) × (-6)}] \]

3. **Evaluate the second innermost bracket**:
- Calculate `(-3) × (-6)`.
\[ (-3) × (-6) = 18 \]
Now, the expression is:
\[ (-12)[-10] ÷ [4{13 - 18}] \]

4. **Simplify the second bracket**:
- Now, calculate `13 - 18`.
\[ 13 - 18 = -5 \]
The expression now looks like:
\[ (-12)[-10] ÷ [4(-5)] \]

5. **Calculate the multiplication in the denominator**:
- Calculate `4 × (-5)`.
\[ 4 × (-5) = -20 \]
The expression now simplifies to:
\[ (-12)[-10] ÷ -20 \]

6. **Calculate the multiplication in the numerator**:
- Calculate `(-12) × (-10)`.
\[ (-12) × (-10) = 120 \]
The expression now becomes:
\[ 120 ÷ -20 \]

7. **Perform the division**:
- Finally, calculate `120 ÷ -20`.
\[ 120 ÷ -20 = -6 \]

Thus, the value of the given expression is **-6**.

### Final Answer:
(a) -6