determiners - When can we omit the preposition "of" in such cases?

I'm struggling to understand when we can omit the preposition "of" in cases when we use determiners in English (distributives and quantifiers).

I mean we all know that both "half the students were absent" and "half of the students were absent" are correct as well as "all my friends are there" and "all of my friends are there".

I would like to know the rule - when can we or can't we omit the "of"?

Scrolling through various examples online I've noticed that even with "all" and "half" it doesn't always apply and sometimes we can use it with other determiners and other times - not:

• Both of the cars were stolen. (can we omit "of"?)


• Half of every apple on the table was bitten. (can we omit "of"?)


• All of it was a lie. (can we omit "of"?)


• Several of my books were printed in Canada. (can we omit "of"?)


• Most of the people living in our town are teenagers. (can we omit "of"?)