Can't set my MacBook Air screen to work independently with an outside screen

Finding mirror: Open System Settings and select Displays. If you have the external display connected you should see a visual representation of both the external display and MBA. Click on the external display and below it you should now see Use as - make sure you don’t have mirror selected. When using an external display with my MBA I make the external the Main display.

More information required. What is the model number and manufacturer of your display and what kind of cable and/or hub are you trying to use? I often connect my MBA to my LG display using a DisplayPort cable and have no problems.

I don’t understand the problem you are describing. What your picture shows is exactly what I’d expect. It appears you’ve clicked on the external display and you now have the option of making it the main display or making it the extended display. You say:

but still when I move from one screen to another on my mac the screen on my display move as well??

but I don’t follow your meaning. Could you give a description. For example, “I open a Word document and it appears on both my MBA and external display.” or whatever it is you are seeing.