Before verbs, this question would be a duplicate as mentioned in the comments. (usually “avant de” + infinitif présent; après + infinitif passé)

Before nouns, “avant” and “après” are directly followed by a “noun group”. This noun group will be composed of “déterminant + nom” like in other situations (like the start of the sentences). There are plenty of “déterminants” that you can use and one of them is “de” (not the preposition in this case, but a contraction of “des” before an “adjectif épithète”). Sentences with “après de” are therefore quite rare, but possible.

Il est parti après de longues heures.

De longues heures se sont écoulées avant qu'il ne parte.