Motor and transmission mounts. Or differential is getting worn(check fluid- sometimes the differential fluid and transmission are shared- if not, refill or youll lose the differential ).
Check the easiest first, the mounts are probably old, worn and broken.
A clunking noise, when you put your car into gear, is most likely caused by a bad u-joint. A problem in the transmission can also cause the noise.
Worn motor and/or tranny mount.
movement of suspension components?
Check for looseness in the front axle u-joints.
I am not sure what you mean by rear, but here are some possibilities. It could be bad u-joints if it makes the sound right when you put it reverse it will could also make it when you put it in drive. If you have the automatic 4L60-E transmission and i only heard this once that the reverse input clutch was so messed up that it made a clunking sound.
A bad gear can cause your four-wheel-drive transfer case to make a clunking sound. The transfer case should be checked immediately.
Most of the time it makes that sound because of bad gas! Put some gas treatment in the gas tank and also some oil treatment wouldn't hurt it either!
A car that is in good running condition should not make a clunking noise. If a person pushes the gas and brake pedal at the same time causing a car to make a clunking noise, that is an indication of stain on the motor.
Drive shaft play/possible worn/bad ujoints /driveshaft
It could be the ball bearings or the ball joints or the breaks but not to sure but that's what it was on mine.
Type your answer here... if it is a front wheel drive it could need c.v.Joint's. Just a thought
Worn suspension parts - struts Loose strut mount?