The noun 帽子 (màozi) means "hat" or "cap." It is a common everyday noun that can be modified by color words or adjectives, as in 红色帽子 (red hat).
出门别忘了戴帽子。
Chūmén bié wàngle dài màozi.
Don't forget to wear a hat when you go out.
这顶帽子是谁的?
Zhè dǐng màozi shì shéi de?
Whose hat is this?
天冷了,你应该戴一顶帽子。
Tiān lěng le, nǐ yīnggāi dài yī dǐng màozi.
It's getting cold; you should wear a hat.