1. **State the problem:** We are given two functions: $$F(x) = 6 + |-2x| - x^2$$ $$G(y) = \left|\frac{-y}{y} - 1\right| - y + 4$$ We need to find $G(c)$ where $c = F(-4)$. 2. **Calculate $F(-4)$:** Substitute $x = -4$ into $F(x)$: $$F(-4) = 6 + |-2(-4)| - (-4)^2$$ Simplify inside the absolute value: $$= 6 + |8| - 16$$ Since $|8| = 8$: $$= 6 + 8 - 16 = 14 - 16 = -2$$ So, $c = -2$. 3. **Calculate $G(c) = G(-2)$:** Substitute $y = -2$ into $G(y)$: $$G(-2) = \left|\frac{-(-2)}{-2} - 1\right| - (-2) + 4$$ Simplify the fraction: $$\frac{-(-2)}{-2} = \frac{2}{-2} = -1$$ So inside the absolute value: $$-1 - 1 = -2$$ Absolute value: $$|-2| = 2$$ Now substitute back: $$G(-2) = 2 - (-2) + 4 = 2 + 2 + 4 = 8$$ 4. **Final answer:** $$\boxed{8}$$