I have a 2004 Accord EX 2.4 automatic. This part where the vacuum hose connects broke and I have no idea what it is called. It is sitting right next to the fuel rail and the wire from the injectors also connects to it.

 

Back up a little bit with the camera - it's hard to tell where that is.
It looks like the "electronic control solenoid" (50391-SDA-A01); #9 in the picture. Not a very descriptive name...


I'm going to move this to General Tech. We use the DIY section for finished write-ups, not for questions like this.

 

That is the engine mount control solenoid valve.

Accords with automatic transmission have a vacuum assisted engine mount. It is used to control excessive vibration at low rpms (e.g. idle). At low rpms, the PCM sends a ground signal (-) to the engine mount control solenoid valve, which opens the valve.

 

OK, now I can show where the hoses are supposed to connect (just in case that was part of your real question...)

The solenoid is at the upper left; and the front engine mount is #9 and the hoses are shown here.