Question

all of the teachers 和all the teachers 哪个对，还是两个都可以

Answer 1

都可以。
All 和all of 有这些用法：
用来表示“所有”或“所有的”
1.名词前面-- 可用all 和all of 形式,两者可以互换：
Has all (of) the cake been eaten?
Have all (of) the presents been distributed?
All (of) my friends have come to my party.
2.代词前面-- 只可用 all of 形式
All of us are going to Sam's party next week.
All of them were singing Happy Birthday.
Has all of it been consumed?
强调性,用来表示“全部”
3.用在形容词或副词前面
Your feet are all wet.Have your boots got a hole in them?
I got scared,ran off and left her all alone.
All around me I could hear people calling her name.
Tell me all about your kayak trip up the estuary..
I got sunburnt and it was all because I didn't have awide-brimmed hat.