How do you evaluate the expression \[8+\left( 36\cdot 8-204 \right)\div 6\]?

Hint: This type of problem is based on the concept of BODMAS. First, we need to look for the operation used in the expression. Here, we have bracket, division, multiplication, addition and subtraction. Solve the operations in the order mentioned above which is from BODMAS. On solving the bracket, we get 288-204=84. Now divide 84 by 6, we get 14. Then, we should add 8 with 14 to find the final value of the expression which is the required answer.

Complete step-by-step solution:
According to the question, we are asked to find the value of the expression \[8+\left( 36\cdot 8-204 \right)\div 6\].
We have been given the expression is \[8+\left( 36\cdot 8-204 \right)\div 6\]. -----(1)
We first have to solve expression (1) with BODMAS, where B stands for bracket, O stands for order, D stands for division, M stands for multiplication, A stands for addition and S stands for subtraction. We are supposed to solve this expression in this order only.
Here, we find that, in the expression given there is bracket, multiplication, division, addition and subtraction.
First, let us consider the bracket \[\left( 36\cdot 8-204 \right)\].
We have to solve this part.
According to the BODMAS rule, we should multiply first and then subtract.
Therefore, we get
\[36\cdot 8-204=36\times 8-204\]
\[\Rightarrow 36\cdot 8-204=288-204\]
Now, we need to subtract.
\[\Rightarrow 36\cdot 8-204=84\]
Substitute this in the expression (1). We get
\[8+\left( 36\cdot 8-204 \right)\div 6=8+84\div 6\]
According to the BODMAS rule, we have to divide now.
We know that \[\dfrac{84}{6}=14\]. Therefore, the expression is
\[\Rightarrow 8+\left( 36\cdot 8-204 \right)\div 6=8+14\]
Now, the only operation left is addition. We get
\[\therefore 8+\left( 36\cdot 8-204 \right)\div 6=22\]
Hence, the value of the expression \[8+\left( 36\cdot 8-204 \right)\div 6\] is 22.

Note: Whenever you get this type of problem, we should always use BODMAS only. We should avoid calculation mistakes based on sign conventions. If we try to solve without BODMAS, we get the final answer wrong. Also don’t consider the dot given between 36 and 8 to be a decimal point. It indicates multiplication.