How do you simplify $4-3\left[ 4-2\left( 6-3 \right) \right]+2$ using PEMDAS?

Hint: PEMDAS is a rule for the order of the mathematical operations in a mathematical expression. It is an acronym which stands for Parenthesis, Exponent, Multiplication, Division, and Subtraction. So according to this rule, we must simplify the expression inside the parenthesis in the given expression $4-3\left[ 4-2\left( 6-3 \right) \right]+2$, which is $4-2\left( 6-3 \right)$. In this, we have again a parenthesis which is $\left( 6-3 \right)$ where subtraction needs to be performed to get $4-2\times 3$. Then, we have subtraction and multiplication in which multiplication needs to be performed followed by the subtraction. After doing all of these, we will have subtraction, multiplication, and addition operations which can be similarly solved according to PEMDAs to obtain the final simplified expression.

Complete step by step solution:
The given expression in the above question is
$\Rightarrow E=4-3\left[ 4-2\left( 6-3 \right) \right]+2$
We know from the PEMDAS rule that we first have to solve the square bracket, which is $\left[ 4-2\left( 6-3 \right) \right]$. Now, in this we again encounter a circular bracket where we have $\left( 6-3 \right)$ on simplifying which we get $3$ and the square bracket becomes $\left[ 4-2\times 3 \right]$. So the above expression can be written as
$\Rightarrow E=4-3\left[ 4-2\times 3 \right]+2$
Now, inside the parenthesis we have subtraction and the multiplication operations, from which multiplication is performed first to get
$\Rightarrow E=4-3\left[ 4-6 \right]+2$
Now, after subtraction inside the parenthesis, we get
$\Rightarrow E=4-3\times \left( -2 \right)+2$
Now, we are having subtraction, multiplication and addition operations. According to the PEMDAS rule, we perform multiplication first to get
$\Rightarrow E=4+6+2$
Now, we are left with only single operation of addition in the above expression which can be easily solved to get the final simplified expression as
$\Rightarrow E=12$
Hence, the given expression is simplified using the PEMDAS rule as $12$.

Note:
We can also solve the given expression using the BODMAS rule, which is more the familiar rule. The PEMDAS and the BODMAS rules are exactly similar. We must note that the parenthesis must be solved first, regardless of whatever operation it contains. For example, inside the square bracket, we were having the expression $4-2\left( 6-3 \right)$ in which the circular bracket has subtraction operation. Although according to the PEMDAS rule the multiplication is performed first before the subtraction, since subtraction is inside the parenthesis, it must be performed first.