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At the top of the photo you’re looking at the vacuum switching valve. The disconnected vacuum hose connects to fuel vapor feed which is the part in the bottom left of the photo.
Look at the photo of the part, it has two male fittings/protrusions, one of them appears to be broken off in the hose in the your original picture. Look at the diagram, the part is highlighted in yellow. You’ll need that part in my photo and a new retaining clip to fix it.
there is no other hose, just that short segment with the broken piece inside it still.
Of course this all assumes the photo by the OP is of a SC430 car part. You never indicated a model of a car.
Last edited by VVTiBob; Feb 8, 2018 at 10:04 AM.
Reason: For clarity of which car model.
If you are getting a Check Engine Light, this break will cause it. The chances are, if you fix this break, another hose will crack. Since the hoses are all the same age, replacing one usually means it is time to replace them all.
Here is a picture of the little box you are looking for
