What do I do on i mac because Microsoft word 2008 is out of support?

Can this 2008 desktop device be upgraded...

What upgrading is possible depends on the exact iMac sub-model and the actual macOS version currently installed ("iOS 10.3.3" as shown in your equipment profile cannot run on Mac computers, only Apple mobile devices). Please do "About this Mac" from your Apple menu to see your current OS version and your iMac sub-model. Although the format of "About..." varies with the OS version, all will show the needed information like in this example:

The red arrow I added shows where to find your sub-model in macOS 10.10. Note the OS version is also displayed. Please do not post your serial number.

If the computer is 2008 your upgrade/update options are limited. If it is 2009 there may be a bit more to work with. That's why we need exact model designations to properly answer your question.

I still use Office 2008 and have no issues with MS Word. It runs fine even under the latest OS version "High Sierra." However, Excel, although functional, now has some little quirks that, while not deal-breakers, can make the sensitive spreadsheet driver nervous.

I have a Mid 2011 27" iMac and am running MS Office 2008 without issue in High Sierra. Granted I don't use all of the features of many of the apps but they all do the basics for me.

Even if it's not supported the software should still work. If you find you need to upgrade at a later date the current Word and Excel docs should be compatible with the newer versions.

Purchase a device newer than 10 years old. You cannot expect technology not to advance - they do at least yearly and it is surprising that your computer still works. I do not know if your MS license will support a transfer to a second computer and you would need to check if it is still compatible with a newer Mac OS system (or upgrade your MS to a more current one).

no matter if you pay for a new version of ms office or if you get free LibreOffice or use apples iWorks or use google docs your current documents will not just be deleted, as far as I know apart from a new ms office LibreOffice is the one most likely to be able to open your current word documents

Personally, I would not spend money on upgrading a 10 year old computer. All the hardware parts will fail sooner or later (including hard drive, logic board, graphics card, etc) and, even with more RAM and/or a faster hard drive, your processor is still an old modelcapacity.

Yes, I would consider a newer computer. As for transferring your files: you will need to see if your apps are compatible with a new operating system; your files can be transferred in various ways as long as you have the app to open them with on the new computer.

Buy a newer version of Office if it will run on that computer, or look into free options such as LibreOffice. I use LibreOffice on a 2008 iMac with Mavericks OS.