This teacher's schedule is all booked up for the next three days.
This teacher doesn't have any openings in his schedule for the next three days.
ーThis teacher's schedule is all booked up for the next three days.
「この先生の予定は３日後までずっと埋まっています。」
be booked up で「予約でいっぱいになっている・先約がある」
for the next three days は「向こう３日間・次の３日間」という意味です。
ーThis teacher doesn't have any openings in his schedule for the next three days.
「この先生は３日後まで全く空きがない。」
予約でいっぱいと言うのとは逆に doesn't have any openings in his schedule「スケジュールに全く空きがない」という言い方もできます。
opening で「空き」
ご参考まで！
カナダ 
