Hi vandanamat,
Thanks for using Apple Support Communities. We understand you have some questions about using an external display. We're happy to share some information to help. When trying to set up to extend or mirror make sure you're using the steps below:
Set up the displays as an extended desktop
You can arrange your displays in any configuration to create an extended desktop. For example, you can set your external display side by side with your Mac to create one large continuous desktop.
Note: You must be connected to a display to see these options.
Set up the displays as an extended desktop
1. On your Mac, choose Apple menu
> System Settings, then click Displays
in the sidebar. (You may need to scroll down.)
2. Click the name of your display on the right, click the “Use as” pop-up menu, then choose “Extended display” or Stop Mirroring.
Set up the displays for video mirroring
Video mirroring shows the entire desktop on each display.
Note: You must be connected to a display to see these options.
1. On your Mac, choose Apple menu
> System Settings, then click Displays
in the sidebar.
2. Click the name of your display on the right, click the “Use as” pop-up menu, then choose Mirror for Display.
See more about that here: Use one or more external displays with your Mac
Thanks.