"Talk through your hat" is an idiomatic expression which means to speak without knowledge or to talk nonsense. If you are looking for synonyms to explain the same term, you could use phrases like "talking out of turn," or "speaking without authority." You can also use the expressions "fabricating," "lying," or "spouting gibberish" to describe someone who is talking through their hat. Other phrases to use include "making things up," "talking off the top of one's head," or "shooting from the hip." If you want to be a bit more polite, you can use terms like "uninformed" or "unfounded".