Q: can i upgrade my older mac  currently running 10.6.8

Maygbe. It depens upon yur Model Mac Mini

A model Macmini1.2 can on only go 10.6.8

A Macmini2.1 to 10.5 (Lion)

A 3.1 or later can go to Yosemeite

See:

How to identify Mac mini models - Apple Support

It all depends on the machine in question, most likely yes.

If yo do not have a Mini then:

- See the following if yo can go to Lion

OS X Lion - Technical Specifications

To see if you can go Yosemite:

http://www.apple.com/osx/how-to-upgrade/

And, it would depend on whether you actually have a MacMini. Since your tag line indicates that you have an iMac.

And if you have any model Mac, the basics include looking into About this Mac

from the Apple (icon) menu in Finder on the desktop, and get more information.

This can tell you the system information or profile of hardware & installed OS X.

Somewhat similar, in how to identify any model, are those basics such shown here:

•How to identify iMac models -- Apple Support

You also could use an online Identify by Serial Number lookup service for your own

information, to see other details or to compare specs if you choose to know more

and cannot navigate Apple sites. A build date of exact detail can be found this way.

And that may make a difference when upgrading hardware to run a later OS X.

•Identify your Mac - Lookup your Mac by Apple Serial Number...

https://www.powerbookmedic.com/identify-mac-serial.php

If you have an iMac, this thread could've been relocated to that ASC discussion area.

However the question really is, if you have a Core Duo model or Core2Duo, and if

the computer can be upgraded in RAM so it may run Yosemite. Or if you may have to

choose to buy a download code to get Mountain Lion 10.8.5 if your Mac is marginal.

Details details. Pesky details. Why are they important?

Do I like to choose to breathe diesel fume or clear air?