1. The problem is to find the maximum integer value of the function $$y = -4^{x+2} - 3$$. 2. Observe that the term $$4^{x+2}$$ is an exponential function with base 4, which is always positive for all real values of $$x$$. 3. Since the function is $$y = -4^{x+2} - 3$$, the exponential part is multiplied by -1, so $$-4^{x+2}$$ is always negative (or zero if $$4^{x+2}$$ were zero, but it never is). 4. The maximum value of the function occurs when $$4^{x+2}$$ is at its minimum, which is the smallest positive value it can get. 5. However, because $$4^{x+2}$$ approaches zero as $$x o -infty$$, the term $$-4^{x+2}$$ approaches 0 from the negative side. 6. Therefore, $$y = -4^{x+2} - 3$$ approaches $$-3$$ from below as $$x o -infty$$. This means the maximum value of $$y$$ (for any real $$x$$) is $$-3$$. 7. Among the integer options given (0, 4, -3, -4), the maximum integer value attained by the function is $$\boxed{-3}$$. Final answer: $$-3$$.