What is this? And where does the hose go?

[RocFox]

I am missing this gray hose. Had a new engine put in look like hose was not put back. Can anyone tell me what is for and where the hose leads.

Thanks,

Rocco

 

[Number4]

Should go into the cab at your heat control. Opens and closes water flow to the heater core?

 

[CDW6212R]

Ditto, that's a vacuum line for the HCV. Find it in the engine bay and make sure it's not open, which is a vacuum leak. It's a fairly long line which could be routed far away.