This problem involves solving a mathematical expression where the standard arithmetic operators have been redefined. We need to carefully substitute the symbols and then apply the correct order of operations (often remembered by the acronym BODMAS/PEMDAS) to find the correct answer.

Understanding the Symbol Replacements

First, let's list the given symbol replacements:

• '+' is replaced by '×'
• '×' is replaced by '÷'
• '÷' is replaced by '–'
• '–' is replaced by '+'

Applying Symbol Replacements to the Expression

The original expression is: 16 + 18 × 3 ÷ 6

Now, we substitute each operator according to the rules:

• Replace '+' with '×': 16 × 18 × 3 ÷ 6
• Replace '×' with '÷': 16 × 18 ÷ 3 ÷ 6
• Replace '÷' with '–': 16 × 18 ÷ 3 – 6

So, the modified expression becomes: 16 × 18 ÷ 3 – 6

Solving the Modified Expression using BODMAS

The BODMAS rule helps us determine the order of operations:

• Brackets
• Orders (powers and square roots, etc.)
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

Let's solve the expression 16 × 18 ÷ 3 – 6 step-by-step:

1. Perform Division: We have 18 ÷ 3.

   Calculation: $$18 \div 3 = 6$$

   The expression now is: 16 × 6 – 6

2. Perform Multiplication: Next, we calculate 16 × 6.

   Calculation: $$16 \times 6 = 96$$

   The expression is now: 96 – 6

3. Perform Subtraction: Finally, we subtract 6 from 96.

   Calculation: $$96 - 6 = 90$$

Final Result

After applying the symbol replacements and following the order of operations, the value of the expression is 90.