$$ \frac{18 \times 14 - 6 \times 8}{488 \div 4 - 20} = x $$

### Concept & Logic This expression requires a straightforward application of the BODMAS rule for both the numerator and the denominator independently. Remember the priority: Division comes before Multiplication, which comes before Subtraction. ### Step-by-Step Solution * **Step 1:** Simplify the numerator. First, perform the multiplications: $ 18 \times 14 = 252 $ $ 6 \times 8 = 48 $ Next, perform the subtraction: Numerator $= 252 - 48 = 204 $ * **Step 2:** Simplify the denominator. First, perform the division: $ 488 \div 4 = 122 $ Next, perform the subtraction: Denominator $= 122 - 20 = 102 $ * **Step 3:** Divide the simplified numerator by the simplified denominator. $$ x = \frac{204}{102} $$ $ x = 2 $ ### Exam Strategy & Shortcut To calculate $18 \times 14$ quickly, you can use the base 10 multiplication trick or break it down algebraically: $ 18 \times (10 + 4) = 180 + 72 = 252 $. Once you see $\frac{204}{102}$, you should immediately recognize that $102 \times 2 = 204$. You do not need to perform long division; simply look at the leading digits and unit digits ($2 \times 2 = 4$). ### Common Pitfall A major mistake is violating the order of operations in the denominator by subtracting before dividing (e.g., trying to do $4 - 20$ first). Always scan for the division symbol and execute it before any addition or subtraction. ### Final Answer **Therefore, the correct answer is 2.**