The vegetable with four words in its name is "cabbage patch kid." While "cabbage" is the primary vegetable, "patch" and "kid" refer to the popular toy line. However, if you are looking for a vegetable name itself, "Chinese long beans" can also be considered, as it has four words if you include the variety descriptor.
Four
beet
veg out = rest
bean
Some four letter vegetables are:beanbeetcornkaleokratarowort
Only using words with 4 or more letters, there are 73 possibilities (including vegetable).ABETABLEAGEEALEEBALEBATEBEATBEETBELTBETABLAEBLATBLETEAVEEGALGALEGATEGAVEGELTGETAGLEELATELAVELEETLEVATAELTALETEALTEELTELATELEVALEVEALVELAABELEAGLEEAGLETBAGELBEGATBEGETBELGABETELBEVELBLATEBLEATEAGLEELATEGABLEGAVELGELEEGLEBAGLEBEGLEETLEAVELEVEETABLETELAEVALETBEAGLEBEETLEBELATEEAGLETGELATEGLEBAELEGATETELEGAVEGETEVELATEELEVATEGETABLELEGATEEVEGETALVEGETABLEIn the word vegetable, there is only one word-vegetable. However, there are 9 letters in the word.15
veg-o
lettuceleeks
spud
beet
Eggplant.
BEAN