1989 jeep 4.2 engine vacuum hoses

It should be on a sticker, in the engine compartment, or the hood,

very very old post
ok i figured your old post out.
you posted a 1981 SJ jeep to jeep grand cherokee section.
this is the early Cherokee and is not grand. 1995+
with no engine stated, wow)
ill not try to guess the engine.
here they are...
258 cu in (4.2 L) AMC I6
360 cu in (5.9 L) AMC V8 2-barrel
360 cu in (5.9 L) AMC V8 4-barrel
401 cu in (6.6 L) AMC V8 4-barrel

made in USA or Australia, ill guess USA

the vacuum setups vary by carb used
and if FED usa or Calif USA setups
fed was called 49 state back when...
and there is the high altitude versions.
and std or HD cooling versions (huge list of vacuum setups, if you want look in alldata.com and behold.
omg one more the Canada version.... (ill skip export versions)
calif versions are huge complex....

so ill guess the 360 2 barrel,

You should have a vacuum line diagram under the hood of your car you can buy the haynes repair book for your vehicle at any autozone or advance auto someplace like that

http://www.autozone.com/autozone/repairguides/Nissan-Pick-ups-and-Pathfinder-1989-1995/ELECTRONIC-ENGINE-CONTROLS/Engine-Co

check for vacuum leaks ---transmission actuator and hose
vent control hoses , any where the there is vacuum control
the idle air control sensor would be a suspect so check wiring , connections and the sensor itself

Start with the basics...meaning check the spark plug wires and spark plugs. While under the hood, inspect all hoses for a vacuum leak(s). Then turn the ignition key on-off-on-off- on...leave in the on position and write down the number of flashes the check engine light indicates....2 flashes = #2....pause.....3 flashes = #3.
Let start from here. Are you able to perform engine repairs or diagnostics???

Sounds like a possibility of a vacuum leak. Inspect the vacuum tubing for damage or wear or just not being connected. One mechanic's trick is to spray carburetor cleaner on the vacuum lines with the engine running. Use safety goggles when trying this. If there is a vacuum leak - when the carb cleaner hits it the engine will speed up.

The powdery black substance tells me that your egr valve is not working.And that is operated by the vacum sysem.The pipe has probebly come of the EGR valve.

This system is run off a vacuum line get under the jeep its on the passenger side a hose runs into the axle housing make sure that it is plugged into the connector.

If you look under there you should find a steel or plastic line that runs up to a place inside the engine bay.( If it is connected directly to the differential) If it is connected to a box mounted on the right side axle it is part lof your 4x4control and should carry vacuum. With engine running you will hear vacuum leak and easily find connection point.
(but you didn't mention any driveline problem so it's likely the first, which is only a vent line. as long as it is not pointing foreward or straight up it is also ok to just secure it out of the way. (but not where it will become submerged in water etc.