hard to say, look at the ball joins , axles and or bushings on the control arm.(look at the boots on the axles. make sure they're not broken)
96 Town car does not have front axles or boots, it's a rear drive car--- the rest of the above answer is reasonable. I have a 96 and a 99 Lincoln and both make this noise. Started when they both had less than 30,000 miles. Have looked, checked, had it in a front end alignment shop, etc etc, but can't find cure. I don't worry about it anymore.
Buick makes a clunking sound from trans area when accelerating.
Sounds like its from one side? Ur shocks
chiken
tie rod
Check the strut mountings Check springs and shocks they may be worn out
Wheel bearings or u joints
could be your crank shaft
age
It's either something loose or something worn out. I'd start with the shocks then look at the ball joints.
replace c/v joints
Wheels are unbalanced or you need a front end alignment.
Very possible it is the right side half shaft.