What is your question?
My question is what type of hinge/linkage i can use to achieve that
That's a very open-ended question with very little definition. What have you tried? Why didn't it work?
I have tried Simple Pivot join it didn't work,and i tried 4 bar linkage but I couldn't figure it out.
I'm thinking that if I can make the green piece slide outward a little bit, then start rotating, it will open without having any collusion issue.
I don't know where to start to be honest, i don't know if I should design it or if such "hinges" already exist or what i need isn't a hinge it's called something else
We might be able to help if you could draw it out to scale.
I think your problem is probably the location of center of rotation. If the centerline of your pivot point is above the red floor then the bottom corners of the two opposed green shells are going to get closer to each other as they rotate upward. If you want everything to pivot with no interference your pivot centerline is going to have to be at the bottom of the green shells. Simple geometry. Draw the arc of motion about various fixed pivot points.
The only problem remaining is that I don't have access to the outside (bottom of red and green shells) I have to join them with a joint above the red floor and inside the green shells but at same the resulting rotation need to be about the outside corner
There are cabinet door hinges that do that. They connect the door to the frame in such a way that when the door opens it pivots about a centerline that is outside the physical boundary of the hinge itself. I think they're called invisible hinges or concealed hinges or something like that. Google it.