upgrade memory on a on an iMac 21.5 inch late 2013

Also, for most 8GB of RAM is adequate. May I ask why you feel your iMac needs additional RAM?

If you are trying to improve performance, adding RAM will not help it. In that case the chances are you may have an entry level iMac with a 5400 RPM HD, that HD is the performance bottleneck. In that case you can add an external SSD such as a OWC Mercury On The Go Pro & a OWC On the Pro Go Power Adapter. Then clone the internal HD to the SSD using a tool such as Carbon Copy Cloner or SuperDuper! and once the clone is done (takes about 1-2 hours) you would set the SSD as your Startup Drive (System Preferences - Startup Disk - Select the new SSD and then restart the computer. The performance difference will be surprising! That being said, please remember a 2013 is considered obsolete, so you may want to simply upgrade by replacing the 2013 with a new 24" iMac. Select one with the highest capacity SSD you can afford and you will have a very fast and capable computer. Another option is to buy a M1 based Mac mini and add your own 27" external display.

The RAM is non user-accessible. You would have to find someone willing to install the RAM. FWIW, that iMac came with either 8GB or 16GB. 16GB is the max.