Install OS X High Sierra on an iMAC 11.3

Model ID "iMac11,3" corresponds to an iMac (27-inch, Mid 2010).

It would have shipped with Mac OS X 10.6.3 or 10.6.4 ("Snow Leopard") and optical discs for use in restoring the original operating system. It can run anything up to macOS 10.3.6 ("High Sierra").

You may need to download El Capitan or Sierra before downloading and installing High Sierra. The El Capitan and Sierra installers are available as .DMG files containing installer applications, and you could use a recent Mac or PC to put a .DMG onto a USB flash drive for transfer to the old iMac. The High Sierra installer is available through the App Store, so the old iMac would need to be running versions of Safari and the App Store that were recent enough (think El Capitan or Sierra) to successfully access the App Store.

Note that in this article:

Create a bootable installer for macOS - Apple Support

the section labeled, "Connect a USB flash drive to your Mac," says:

When you create the bootable installer, this volume will automatically be erased.

Be sure there is nothing you need on the flash drive before trying this option.

Hi,

Following article could help your question.

How to download and install macOS - Apple Support

Just Right click on it & choose open.