There is no 10.13.8 version of High Sierra. The latest version is 10.13.4.
Check compatibility of High Sierra with your device, storage, etc also to make sure this OS is comparable for your iMac:
Regarding recovery mode, you may need to put it in internet recovery mode manually using a different set of keys:
Newer Mac computers and some older Mac computers automatically try to start up from macOS Recovery over the Internet when unable to start up from the built-in recovery system. When that happens, you see a spinning globe instead of an Apple logo during startup. To manually start up from macOS Recovery over the Internet, hold down Option-Command-R or Shift-Option-Command-R at startup.
If you still can't start up from macOS Recovery, and you have a Mac that is able to start up completely, you might be able to create an external Mac startup disk to start up from instead.
macOS Recovery over the Internet, the Reinstall macOS utility, and the Get Help Online utility all require an Internet connection. If you need to connect to a Wi-Fi network, move your pointer to the top of the screen, then choose a network from the Wi-Fi status menu .
Published Date: Sep 26, 2017