Older Mac Needs Updated Java

Java Update 16 is for Mac OS X 10.6 (Snow Leopard)(SL)
You will need to upgrade to Snow Leopard to get that Java SE 6.
Very easy to purchase Snow Leopard direct from Apple.
http://store.apple.com/us/product/MC573Z/A/mac-os-x-106-snow-leopard
Less than $20
And, you can see that you will need to have an intel processor to do that upgrade to 10.6

I suspect that (still running 10.5.8) you have a PowerPC, such as a G4, or a G5.
Which Mac model do you have?

 

Just to finish the point being made here, snow leopard cannot be installed on a G4 or G5. You would need to either buy/borrow another machine to undertake the course.

 

It may well be that the OP can indeed install Snow Leopard. I recently installed SL on a Core2Duo iMac (an Intel Mac rather than PowerPC) running 10.4.

To the OP: What Mac do you use? If you're not sure whether it's PowerPC or Intel, click on the Apple icon in the menu bar at top of the screen. It'll show you what sort of processor your computer uses: PowerPC or Intel. If it's the latter, you can install Snow Leopard on it.