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I was getting my exhaust fixed and the drive shaft that powers the 4x4 is wobbling, what is the correct name of this part.. anyway I think the male and female parts are bad worn, anyone have this. the u-joints are solid it is loose on the spline.

Its your front driveshaft, mine does the same thing. I havn't got a chance to look at yet, so I couldn't tell ya whats wrong with it

would this problem cause the 4 wheel to pop out of gear?

It wouldn't "pop out of gear". Driving normally in 2wd your rear drive shaft transfers torque to your rear differential then too your rear 2 wheels to spin, your 2 front just spin, theirs no direct torque application. When you engage 4wd, torque is applied through your front driveshaft to your front differential too your wheels, so you can get that extra traction and power. Without that front driveshaft you could only have 2wd, even if it was engaged in 4wd, because their would be nothing transfering mechanical energy to your front differential. If it's wabbly like mine, it's at risk to break, it would not affect your gears. I found one in a junkyard in tumwater WA for $25. Too bad I didn't have the tools with me too take it off.