<If you want to know your own vacation days you can go to Settings -> Calendar and it says how many days you have left.
If you mean other player's days... well, then you can't know... (I really think there should be a way too)

When a game times out, that day is set as a vacation day. If another game times out 5 mins later, it will notice that day is already set as a vacation day and automatically extend itself, without spending another day.