1. **State the problem:** Evaluate the expression $$4x^2 - by^2 - by$$ for $$x=2$$, $$b=\frac{1}{2}$$, and $$y=-3$$. 2. **Write the expression with substituted values:** $$4(2)^2 - \frac{1}{2}(-3)^2 - \frac{1}{2}(-3)$$ 3. **Calculate each term:** - $$4(2)^2 = 4 \times 4 = 16$$ - $$\frac{1}{2}(-3)^2 = \frac{1}{2} \times 9 = 4.5$$ - $$\frac{1}{2}(-3) = -1.5$$ 4. **Substitute these back into the expression:** $$16 - 4.5 - (-1.5)$$ 5. **Simplify the subtraction of a negative:** $$16 - 4.5 + 1.5$$ 6. **Perform the addition and subtraction:** $$16 - 4.5 + 1.5 = 13$$ **Final answer:** $$13$$