What kind of なる is correct ?

Ok, so with this grammar point, my Japanese school text book teach me that some thing happens that out of your hand or become they will use this grammar:

I adjective:イ形容詞+の+に+なる。

Na adjective:ナ形容詞+なの+に+なる。

Noun: 名詞+に+なる。

Verb:動詞+こと+に+なる。

But when I google the grammar point it seems not correct. Anyone please explain it to me?

by Comfortable-Ad9912