Preposition is the hardest part, a rule?

Preposition is the pride of one of the English authorities of China, Professor Xu Menxiong, who wrote a recommendation letter for me because he was my father's teacher.

I'm writing on this subject now. In front me is a book, A Glossary Of Phrases With Prepositions by a professor of Colombia Univ. Thomas Crowell Jr., I will try do a further explanation.

It is said that there is no fixed rule for preposition to follow, I'll challenge this saying, partially at least.

Solved "approach to vs. appropriate for"

I'd like to hear your opinion.