$\text{The value of}\mathrm{ 52}-[18÷3+3+(18-11\left)\text{ of }4\right]\text{ is equal to:}$

The correct answer is 15.

To evaluate the given mathematical expression, we follow the BODMAS rule, which dictates the order of operations: Brackets, Orders/Of, Division, Multiplication, Addition, and Subtraction.

The given expression is:

$52-[18÷3+3+(18-11\left)\text{of}4\right]$

Step 1: Simplify the innermost parenthetical bracket.

$18-11=7$

Substituting this result back into the expression gives:

$52-[18÷3+3+7\text{of}4]$

Step 2: Evaluate the "of" operation.
The operation "of" signifies multiplication and takes precedence over standard division and addition within brackets.

$7\text{of}4=7\times 4=28$

Updating the expression inside the brackets:

$52-[18÷3+3+28]$

Step 3: Perform division inside the square brackets.

$18÷3=6$

Updating the expression:

$52-[6+3+28]$

Step 4: Perform addition inside the square brackets.

$6+3+28=37$

Updating the expression:

$52-37$

Step 5: Perform final subtraction.

$52-37=15$

Thus, the final value is equal to 15.