1. **State the problem:** Evaluate the expression $\sqrt{144} - |3^2 - 4 \times 6|$. 2. **Recall the formulas and rules:** - The square root $\sqrt{a}$ is the non-negative number which, when squared, gives $a$. - The absolute value $|x|$ is the distance of $x$ from zero on the number line, always non-negative. - Order of operations: calculate exponents and multiplication before addition or subtraction. 3. **Calculate each part:** - $\sqrt{144} = 12$ because $12^2 = 144$. - Calculate inside the absolute value: $3^2 = 9$ and $4 \times 6 = 24$. - So, $3^2 - 4 \times 6 = 9 - 24 = -15$. 4. **Apply the absolute value:** - $|-15| = 15$. 5. **Combine the results:** - $12 - 15 = -3$. **Final answer:** $-3$