Evaluate: \[ - 8 - \{ - 6(9 - 11) + 18 \div - 3\} \] .

Hint: Since there are more than 2 mathematical operations, we use the BODMAS rule (Ordering mathematical operations). That is Brackets, the part of calculation inside brackets always comes first. Order, we calculate the number involving powers or square root. Then followed by Division, multiplication, addition and subtraction

Complete step-by-step answer:
Given, \[ - 8 - \{ - 6(9 - 11) + 18 \div - 3\} \] this can be also written as
 \[ = - 8 - \{ - 6(9 - 11) + \dfrac{{18}}{{ - 3}}\} \] .
First we need to do the calculation inside the brackets,
We can see that in the brackets we have division operation and then subtraction.
 \[ = - 8 - \{ - 6(9 - 11) + ( - 6)\} \]
 \[ = - 8 - \{ - 6( - 2) + ( - 6)\} \]
We know that multiplication of two negative number gives us a positive number, applying multiplication operation we get:
 \[ = - 8 - \{ 12 - 6\} \]
Subtracting inside the bracket, we get,
 \[ = - 8 - 6\]
Taking negative as common we get,
 \[ = - (8 + 6)\]
Adding, we get:
 \[ = - 14\] is the required answer.
Hence, \[ - 8 - \{ - 6(9 - 11) + 18 \div - 3\} = - 14\]
So, the correct answer is “-14”.

Note: For a calculation that has only one mathematical operation with two numbers, it is a simple case of either adding, subtracting, multiplying or dividing to find your answer. If we have several numbers, and different operations we need to use the BODMAS rule. If we do the above problem without following BODMAS rule we get the wrong answer. In some textbooks they will mention BIDMAS instead of BODMAS. Both are the same. In BIDMAS ‘I’ means indices which is the same as Order. This rule is applied for all the calculations in math.