1. **Stating the problem:** Simplify and evaluate the expression $$12 - (-3) \times \left\{ \frac{1}{4} \div \left[-\frac{1}{2}\right]^2 \right\}$$. 2. **Recall the order of operations:** Parentheses and brackets first, then exponents, followed by multiplication and division from left to right, and finally addition and subtraction. 3. **Evaluate the exponent:** $$\left[-\frac{1}{2}\right]^2 = \left(-\frac{1}{2}\right)^2 = \frac{1}{4}$$ because squaring a negative number makes it positive. 4. **Simplify inside the braces:** $$\frac{1}{4} \div \frac{1}{4} = 1$$ since dividing a number by itself equals 1. 5. **Multiply:** $$-3 \times 1 = -3$$. 6. **Substitute back into the expression:** $$12 - (-3) = 12 + 3 = 15$$. **Final answer:** $$15$$