1984 Cutlass v8 clunking rear
 

I am working on my moms 1984 Olds with only 21K miles.... There is clunking sound coming from the rear when I depress the breaks..
I lifted the rear end on jacks and I put the vehicle on drive. When it's in park I press/depress the breaks and no clunking... When I put it in drive, the right wheel spins - left one doesn't . If I accelerate both spin but when I apply the breaks and depress I hear the clunking noise. Could the culprit be the rear universal joint ?

Thanks for your help.

That sound like a brake issue. You're going to have to pull the wheels off and start checking things out. It COULD be a U-joint, but start with the brakes.