$\text{The value of}\mathrm{ \; 64}[44-(8\text{ of}\mathrm{ 3}-16)4\times 20]\text{is equal to:}$

The correct answer is 16.

Step 1: Understand the order of operations (BODMAS / PEMDAS)
To simplify the mathematical expression, we follow the standard BODMAS rule (Brackets, Orders/Of, Division/Multiplication, Addition/Subtraction):
1. Solve operations inside the innermost parentheses first, prioritizing the "of" operation.
2. Perform division and multiplication inside the brackets from left to right.
3. Perform subtraction inside the brackets.
4. Finally, perform the outer division.

The given expression is:

$64÷[44-(8\text{ of }3-16)÷4\times 20]$

Step 2: Evaluate the expression inside the inner parentheses
First, calculate the "of" operation, which represents multiplication:

$8\text{ of }3=8\times 3=24$

Now, subtract 16 from 24:

$24-16=8$

Step 3: Substitute the value back into the main expression
Replacing the inner parenthetical expression with 8 gives:

$64÷[44-8÷4\times 20]$

Step 4: Solve inside the square brackets
Following BODMAS, division and multiplication are evaluated from left to right. First, perform division:

$8÷4=2$

Next, perform multiplication:

$2\times 20=40$

Now, perform the subtraction inside the bracket:

$44-40=4$

Step 5: Perform the final division
Finally, divide 64 by the result obtained inside the bracket (4):

$64÷4=16$

Thus, the value of the given expression is equal to 16.