1. **State the problem:** Solve the equation $4^{x+2} + 4 = 2$ for $x$. 2. **Rewrite the equation:** $$4^{x+2} + 4 = 2$$ 3. **Isolate the exponential term:** $$4^{x+2} = 2 - 4$$ $$4^{x+2} = -2$$ 4. **Analyze the equation:** Since $4^{x+2}$ is an exponential function with base 4 (which is positive), it can never be negative. 5. **Conclusion:** There is no real solution because $4^{x+2}$ cannot equal $-2$. **Final answer:** No real solution exists.