I need to know the name of this part and also where the other end of the cable in the picture goes. Had to fix a leaking problem by replacing hoses that connect to this piece but now other end of the long cable isn't connected to anything.

 

Looks like your heater control valve.

The "cable" is actually a vacuum line; the control head in the dash routes vacuum to all the little doors that control air flow, and to that thing, to control whether hot water flows through the heater core.

I don't recall whether applying vac to it tells it to open it up, or tells it to close.

 

But i need to know where the other end goes to. Right now it's not connected to anything.

 

Other end of what?

 

The vacuum line. The one end is connected to the top of the heater control valve and the other side is connected to nothing.

 

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Look at the small harness that comes through the firewall right below the heater hoses. It's the complete assy for the HVAC, including both wires and vacuum lines. Should be easy enough to find it in there. There's 2 vac lines; one is purple, and is the "supply" line to the control head. The other is the one for the valve and is some other color (white IIRC).