Is there a trick to knowing when to use ‘de’ after a preposition?

First of all, I'm trying to learn Colombian Spanish. I'm at the beginning stages of learning basic sentences with my Spanish teacher, and every time I see 'of,' I want to use 'de,' but that isn't how it always works. My teacher is teaching me some of the prepositions, and how de will always follow them, for example:

  • alrededor de
  • Después de
  • Antes de
  • Dentro de

Yet, there are other prepositions where de does not follow. Is there a guide that helps me understand when de is and isn't used in a sentence? Looking around on Google makes me even more confused about 'de' and when it actually should be used in a sentence, not just with prepositions, but in general I guess.
Muchas gracias for any help given.

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