IMAC can't boot

When I try to reinstall the operating system it only gives me my external drive that I use for my back ups as an option to install the new operating system. So, again, it does not seem to be able to locate the internal drive.

It looks like the moderator deleted my last linked from dropbox screenshot for some reason. here it is again.

Yes. But once I am there and try to reinstall the operating system or recover with time machine, it can’t find the internal disc

Here is a shot once I get into Recovery mode

https://www.dropbox.com/s/jp8n011yd0cdja8/Screen%20Shot%202021-01-05%20at%2011.47.22%20AM.png?dl=0

Here is when I try to use Time Machine to restore.

https://www.dropbox.com/s/nwi6zmftasakg1d/IMG_2439.jpeg?dl=0

Here is a screen shot when I go to the next step and the machine can not find the internal disc to restore.

[Link Edited by Moderator]