If "+" denotes "divided by", "×" denotes "added to", "÷" denotes "subtracted from" and "−" denotes "multiplied by", then what is the value of 54 + 162 − 18 × 12 ÷ 6?

Introduction / Context:
This question involves coded arithmetic operations where each familiar symbol stands for a different operation. You must decode the expression to reveal the true arithmetic being performed and then evaluate it using standard rules. This improves precision with operator substitution and cautious stepwise calculation.

Given Data / Assumptions:

- "+" denotes "divided by".
- "×" denotes "added to".
- "÷" denotes "subtracted from".
- "−" denotes "multiplied by".
- The coded expression is: 54 + 162 − 18 × 12 ÷ 6.
- After decoding, standard arithmetic precedence (division and multiplication before addition and subtraction) is applied.

Concept / Approach:
We translate each symbol into its true operation while keeping the numbers in the same order. In many exam contexts, when a symbol denotes an operation like subtraction or division, it is treated as a normal binary operator with the same left to right orientation as usual. After this translation, we simplify the resulting expression carefully, respecting operator precedence.

Step-by-Step Solution:
Step 1: Decode each symbol. "+" denotes "divided by", so 54 + 162 becomes 54 ÷ 162. "−" denotes "multiplied by", so − 18 becomes × 18. "×" denotes "added to", so 18 × 12 becomes 18 + 12. "÷" denotes "subtracted from", and in many such coded questions it is treated as subtraction, so we interpret the last operation as minus 6. Putting these together, the decoded expression becomes: 54 ÷ 162 × 18 + 12 − 6. Step 2: Evaluate division and multiplication first. 54 ÷ 162 = 1 ÷ 3 (since 54 ÷ 162 simplifies to 1 ÷ 3). (1 ÷ 3) × 18 = 18 ÷ 3 = 6. Now the expression reduces to: 6 + 12 − 6. Step 3: Perform addition and subtraction from left to right. 6 + 12 = 18. 18 − 6 = 12.

Verification / Alternative check:
A quick check of the arithmetic shows no step was miscalculated. The fraction 54 ÷ 162 correctly simplifies to 1 ÷ 3, and multiplying by 18 indeed gives 6. Adding 12 and subtracting 6 gives 12, which is one of the provided options. Reconfirming the symbol mapping ensures we have not mistaken any operation.

Why Other Options Are Wrong:
Options 4, 16, and 10 could only arise if:

- The coded operations were misread, for example treating "+" as real addition or "−" as real subtraction, or
- Operator precedence was ignored and the expression was evaluated strictly left to right.

Because our calculation adheres to the exact mapping and correct arithmetic rules, those alternate results are not acceptable.

Common Pitfalls:
It is easy to revert unconsciously to the usual meanings of +, −, ×, and ÷, or to forget to simplify fractions fully before multiplying. Another frequent error is to misinterpret "subtracted from" and reverse the order of subtraction. Reading the mapping carefully and rewriting the entire expression with standard symbols before evaluating helps avoid these issues.

Final Answer:
Under the given code language, the value of 54 + 162 − 18 × 12 ÷ 6 is 12.