The title of the essay is "Linguistic Analysis and Language Teaching". The example sentences are quoted from section 9 of the essay, whose topic is as follows: The pragmatic difference between "I called up the doctor" and "I called the doctor up".
OK, so the topic appears to be any difference caused by separating the two halves of a phrasal verb. The phrasal verbs in the original are "put on", "take off", "clean up" and "bring over". The author has confused the issue by adding unnecessary words to the example sentences, and they've particularly messed up the one about vegetables. The two sentences should have been:
He would bring over all the vegetables.
He would bring all the vegetables over.
With regard to Tarheel's comment about the doctor example, I think this is a BrE v AmE difference. In the UK, "phone up/ring up/call up" are all used to mean "to telephone". The word "up" is, admittedly, redundant in all three.
I'm going to phone the doctor = I'm going to phone up the doctor/phone the doctor up
I'm going to ring the doctor = I'm going to ring up the doctor/ring the doctor up
I'm going to call the doctor = I'm going to call up the doctor/call the doctor up