You are approaching a surprisingly broad and complicated problem. To make things worse, you ask for vague directions using vague terminology. I have no idea what should I really write you, from your 10,000 ft view everything seems nice already...

From this 10,000 ft view, what you need is a list of each with a condition to be satisfied. You understand this might be a list... or a tree... of some structure.

So, only interesting advice. Don't think "in general". It will make your head hurt and your workload explode. Define with reasonable precision what you need to make your game work. It is important you have a clear picture of your needs before you start. Take for granted you will be able to do it and draw or write the story on a piece of paper.

In general, you will need sequences and conditions, with some logic operators.

Here is an example: "this door (unique name "RGBKeyedDoor") opens only if player has red, green and blue keys".

Solution 1: Every time a key is picked up it tells RGBKeyedDoor it has been picked up

Solution 2: When RGBKeyedDoor is approaches it does getPlayerInventory(), then find("red key"), find("blue key"), find("green key").

The two things of course are NOT the same.

This "event manager" you have read about it's not the solution. At best, it's part of the solution.