Mother-in-laws

While changing oil & air filter on mother in laws 2002 acura TL I noticed a hose disconnected . There are 2 hoses which come from the round black plastic valve(?), In the 2nd picture, this is located close to shock mount drivers side. The 2 hoses run together (picture 1) then one goes to bottom of engine and other goes to firewall where it is not connected to anything.
Anyone tell me what this hose is and what should it connect to.
Thanks.

Skirmich

That seems to be the purge valve solenoid for the Hydraulic Engine Mounts.. Look at the base of the rear Engine Mount it should have a tube coming out from it, That tube connects to that valve.