You're confusing preposition and "prepositional verbs".
Multi-word verbs are verbs which consist of a verb and one or two particles or prepositions (e.g. up, over, in, down). There are three
types of multi-word verbs: phrasal verbs, prepositional verbs and
phrasal-prepositional verbs. Sometimes, the name ‘phrasal verb’ is
used to refer to all three types.
For example, I've found where you have gotten your quote from and it even provides a table of "prepositional verbs". Notice how the "prepositional verb" which consists of the verb and preposition next to each other and cannot be separated:
- italics are the verbs
- bold are the prepositions
At what are you looking?
After whom are you looking?
From what did you prevent me?
Of what are you accusing me?
In these sentences, they are prepositions and the verbs are clearly separated and so are not prepositional verbs, so the initial statement about:
"Prepositional verbs have two parts: a verb and a preposition which
cannot be separated from each other."
does not apply.
Furthermore, they can be reworded so that the preposition shifts to the
What are you looking at?
Whom are you looking after?
What did you prevent me from?
What are you accusing me of?
- (5) look at and (6) look after are not prepositional verbs, though they can be.
- in (5) to (8), the object of preposition is the wh-phrase.
- prepositional verbs which are used transitively can be separated
- prepositional verbs which are not used transitively cannot be separated
- look at and look after are both transitive-prepostional verbs
Prepositions vs preposition verbs:
Usually, transitve-prepositional verbs don’t make sense without an object.:
He looked at ______ .
It’s hard work looking after _______ .
The preposition (particle) cannot be moved/reversed most of the time in prepositional verbs:
✓ He looked at her.
✗ At her he looked.
✓ It’s hard work looking after three children all day.
✗ Looking after three children all day it's hard work
Prepositions vs Phrasal verbs https://www.temple.edu/writingctr/english-language-learners/documents/Prepositionsvs.Prepositionalphraseshandout.pdf