Learn Portuguese (Portugal): Bebe chá quente para a garganta.

The word Bebe is being used as an informal command, also known as the imperative. To tell someone to do something using the informal tu, you take the normal present tense form bebes and drop the final -s. If you were giving a formal command to você, you would change the ending completely and say Beba.

The English translation says 'your throat', so why does the Portuguese sentence just say a garganta (the throat)?

In Portuguese, you generally do not use possessive words like tua or sua when talking about body parts. Instead, you just use the definite article, which in this case is a. Because you are giving advice directly to the person, context makes it perfectly clear whose throat is hurting!

Why do we use the preposition para in this sentence instead of por?

You use para here because it expresses the purpose, goal, or intended recipient of the action. The hot tea is specifically meant to benefit the throat. The word por is usually used to talk about a cause, a route, or an exchange, which does not fit the meaning of this sentence.