throttle body" fuel", cooling system separate.
On a 3.8 engine the throttle body and upper plenum contain coolant. There is a gasket between them that could leak. More important the upper pleninum on the 3.8 engine often develops a leak near the EGR inlet which is in the area you are concerned with.
You will need to remove the throttle body and replace the throttle body gasket. The throttle body gasket can be purchased at most auto-parts stores.
Check the throttle body over carefully to find the leak. If a gasket is leaking then a new gasket set will stop the leak. If the body has a crack then you will need to replace the throttle body.
You have a coolant leak.You have a coolant leak.
Look for a vacuum leak. With the engine idling, anywhere you have a vacuum hose attached, Spray some throttle body cleaner at the connections and see if the engine idle picks up even just a bit. If it does, you have a vacuum leak. After checking if you do not find anything, at least spray some throttle body cleaner in the throttle body and clean the throttle blade up. Also try the Idle air Control Valve Located on top of your throttle body, or even the throttle position sensor
Check for a vacuum leak or sticking butterfly valve at the throttle body, or possibly a sticking throttle linkage or throttle cable.
vacuum leak, check the gasket under the throttle body for a vacuum leak. Spray some carb cleaner around the base of the throttle body while the engine is running. If there is a vacuum leak you will hear a change in the rpm's when you hit the right spot.
Could be a vacuum leak. Check the throttle body base gasket.
LeakCheck where the coolant lines go to the throttle body you may have a leak that only presents itself under pressure, as long as the coolant isn't being burnt in combustion in which case you may have a head gasket issue.
The coolant will normally leak into the oil or into the cylinder
Because some opening formed which is allowing coolant to leak out.
A vacuum leak can do that. Check the gasket at the base of the throttle body for leaks. It was common for that gasket to crack and allow a vacuum leak. With the engine running, spray carb cleaner around the base of the throttle body. If the idle changes briefly while you are spraying that area you have found the leak.
Assuming you have throttle body injection, you may have a faulty/dirty injector. Give us more info such as the year, make, model and engine to help us help you.