Multi_Managers do just what you think they would, they manage multiple entitys so you can keep track of them more easily and trigger multiple events to occur when the multi_manager is set off. I'll walk you through the steps of using a multi_manager below.
First I'll start by turning the doors into separate func_door entities. I'm not going to go through the exact settings of func_doors because if you don't already know them than this article is not for you, I'll cover them in another article. I called the door on the right door1 and the door on the left, door2.
Next, I turn the button brush into a func_button and set it's target to mm1. This is what you'll be naming the multi_manager. Again I won't go through every setting in the func_button because that's for more of a basic article.
Now make a multi_manager entity and as said before, name it mm1 (this is what I usually call my managers, for ease). After you've named it you have probably noticed there are no other settings, this is because we create them. Click smart edit in the entity properties and you should see some new info fields appear on the right. Click the 'add' button and a window will appear. In the Key field goes what entity you want to trigger. I want to trigger the first door, and we named it door1, so I'll put that in the Key field. The next field is Value. This is how long (in seconds) the multi_manager will wait before triggering the entity in the Key field. I want it to wait 5 seconds after I press the button until it opens the door, so I'll put 5 in the Value field.
Press OK and your button should now open door1 after 5 seconds of pressing the button. Repeat the last step for door2, changing the value depending on how long you want it to take for the door to open.
That's it! multi_managers are very powerful and I use them in almost every single map I make. With them, the possibility's of what can be created with hammer are, literally, endless.
Well I hope this was informative and helpful. Leave a comment if you need help or would like to suggest a future article!