Loud clicking noise when 4h and 4low are engaged

Welcome to 2CarPros. If you only get the clunk in 4WD then it is either in the transfer case or the front driveline in either the driveshaft or the front differential or it's axles. The image of the transfer case shows the internals, usually they don't clunk, they just stop working.
The items I would look at first would be the front driveshaft between the transfer case and front differential. The U-Joints would be the first things to look at like in the third image.
You should not be able to move the parts in relation to each other. Then check the outer front axles. I wouldn't think they would only make noise in 4WD though. To remove them you remove the 4 bolts that hold the flanges on. Then replace the joints and torque the bolts to 54 ft. Lb.