bank requires browser upgrade to 6.x. I have 10.6.8. Do I need an upgrade?

Yes.

Open the App Store then select Updates from the menu top of the App Store window.

If no updates are available, an alternative would be to use a different browser such as Firefox.

Keep in mind, Apple has not provided any security updates for v10.6.8 Snow Leopard in several years. It's a very outdated Mac OS X. You might consider upgrading to a new Mac for better security.

Upgrade the OS.

Check that your computer is compatible with Mountain Lion/Mavericks/Yosemite/El Capitan.

To check the model number hold down the option/alt key, go to the Apple menu and select System Information.

iMac (Mid 2007 or newer) model number 7,1 or higher

Your Mac needs:

OS X v10.6.8 or OS X Lion already installed

2 GB or more of memory (More is better - 4 GB minimum seems to be the consensus)

8 GB or more of available space

Check to make sure your applications are compatible. PowerPC applications are no longer supported after 10.6.

Application Compatibility

Applications Compatibility (2)

Do a backup before installing, preferable 2 backups on 2 different drives.