Slammed (adj) meaning
In a movie I heard this word which is not present in some dictionaries. One dictionary says that it means that you have too much work that you cannot cope with.
The passage of the movie is the following:
A: Do you know if we can go to dinner next Monday?
B: Oh, I am so slammed next week.
Can you come up with a synonym? Is it just an informal word or very informal? Used in British and Ame?