That T in your pic looks less like a coolant line and more like a vacuum line, but it's hard to tell what I'm looking at from the crop of the photo. Coolant lines will always have a hose clamp on them, the type you need a screw/nut driver to tighten or loosen. Coolant systems are subject to high pressures so tension clips are seldom ever used, push on fittings never.
On those 3.0's there's a line that comes off the engine near around where the t-stat is (where upper radiator hose goes into the engine block) that loops around the back of the engine and goes into the heater core.
Remove the entire air cleaner plastic hose assembly from the throttle body then trace the line, or lines as there may be a bypass line. The lines may, or may not, go to metal at some point, then back to rubber to make the bend into the firewall. The hose that loops around from the block near the thermostat, with hose clamps on it, that goes into your firewall is the inlet, and will usually be the one on the drivers side if it's a side by side*. The outlet/return line will come out about 6" to the left of it (side by side) and go around the engine, to the passenger side, and will go back behind where your belts are to the water pump. If there is a bypass line there will be a Y joining those two lines together before the water pump.
Be aware that the cap on those T's with the flushing kits may end up leaking in the future, they may also hold fine, but YMMV. It's best to cut the old line and put in the T to flush with, then buy a new line to replace the cut one with. Hold on to the line with the T in it b/c you can always use it later to flush with again.
Also, if the engine/radiator is really dirty there's always the chance you may screw up the thermostat by getting flush debris lodged in it.
*If's it's an over/under heater core, then I don't have a clue, and you'll be best served by tracing.