I am trying to download High Seirra on an IMAC Computer with MAC OS Sierra 12.6 operating system. The download does not complete.

Check in your Downloads folder or Applications folder and find and delete "Install Mac OS High Sierra". Then restart and try again. Use this link:

Get macOS High Sierra

Are you getting any error messages that is preventing the download from starting or it starts to download, and then, stalls at some point afterwards?

Which exact model is your iMac and what version of OS X or macOS is it running now?