Find the value of

$[9+3-2\times \{(4÷\frac{1}{4})-4\}+81÷9+81÷9+3-9]+9.$

The correct answer is 9.

To find the value of the given expression, we follow the order of operations (BODMAS/PEMDAS rule), which dictates that we simplify expressions in the following order: Parentheses/Brackets, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

The given expression is:

$[9+3-2\times \{(4÷\frac{1}{4})-4\}+81÷9+81÷9+3-9]+9$

Step 1: Simplify the innermost parentheses.
We first calculate the division inside the round parentheses:
$4÷\frac{1}{4}=4\times 4=16$

Substituting this back, the expression inside the curly braces becomes:
$\{16-4\}=12$

Now, substitute this value back into the main expression:
$[9+3-2\times 12+81÷9+81÷9+3-9]+9$

Step 2: Perform multiplication and division inside the square brackets.
Let us calculate the multiplication and division terms:
$2\times 12=24$
$81÷9=9$
$81÷9=9$

Substituting these values back into the expression:
$[9+3-24+9+9+3-9]+9$

Step 3: Perform addition and subtraction inside the square brackets.
Let us evaluate the terms inside the square brackets from left to right:
$9+3=12$
$12-24=-12$
$-12+9=-3$
$-3+9=6$
$6+3=9$
$9-9=0$

Thus, the value inside the square brackets is 0.

Step 4: Final calculation.
Now we add the final term outside the brackets:
$0+9=9$

Therefore, the final value of the expression is 9.