How to understand the following sentence structures?
Hi, I have a little problem about Dutch sentence structures when I read P110 of Essential Dutch Grammar
On page 110 there are three phrases like these:
mogen ..van
moeten..van
niet hoeven...van
I know that mogen, moeten are modal auxiliaries which mean "may" and "must"
but what is the function of "van" here...
The examples are given the next page however, I don't quite get the meanings of these example sentences
Dat mag je niet van moeder. Mom says you are not allowed to do that
word-for-word translation That may I not of/from mother....
But in the above english translation there are verbs "allow" and "say", but I don't see "allow"and "say/zeggen" in that dutch sentence.

Question

How to understand the following sentence structures?
Hi, I have a little problem about Dutch sentence structures when I read P110 of Essential Dutch Grammar 
On page 110 there are three phrases like these: 
mogen ..van
moeten..van
niet hoeven...van
I know that mogen, moeten are modal auxiliaries which mean "may" and "must"
but what is the function of "van" here...
The examples are given the next page however, I don't quite get the meanings of these example sentences
Dat mag je niet van moeder.> Mom says you are not allowed to do that
word-for-word translation> That may I not of/from mother....
But in the above english translation there are verbs "allow" and "say", but I don't see "allow"and "say/zeggen" in that dutch sentence.

Answer

The verbs "mogen … van" (to be allowed, may), "moeten …. van" (to have to) en "niet hoeven … van" (don't have to) are used to indicate if something is done compulsory or permitted.

The word "van" is used to say who has (or hasn't) given the permission (allowing you) to do something, in the example this person would be "mom".

Dat mag je niet |van moeder|.  
|Mom say's| you are not allowed to do that.

This sentence can't be literally translated in English. So therefor the word "say" is used (when mom doesn't give her permission, she actually has to say it).

If "van" wasn't used, then you could translate the sentence like this:
Dat mag je niet.
You're not allowed to do that.

I hope this was helpful.