This is the 11515th most frequent Korean word.
나가도
"나가도" means "even if (someone) goes out" or "even if (someone) leaves."
In this sentence, '나가도' is used in the sense of allowing or giving permission to go out.
너 나가도 괜찮아.
You can go out if you want.
Here, '나가도' emphasizes the action of going out despite certain circumstances, conveyed by '비가 와도' (even if it rains).
비가 와도 나가도 돼요.
Even if it rains, you can go out.
In this case, '나가도' discusses the potential action of going out and its implications on safety.