From Behind (из-за)
To describe movement originating from behind an object, Russian uses the compound preposition из-за. Just like the basic preposition из (out of / from), из-за requires the following noun, pronoun, or adjective to be in the Genitive case.
You will frequently see this preposition when people, animals, or things peek out (выглядывать / выглянуть) from their hiding spots.
From Under (из-под)
Similarly, when someone or something emerges from underneath an object, you must use the compound preposition из-под. This preposition also strictly requires the Genitive case.
This is commonly used with verbs for reaching, taking, or fetching things out of tight spaces, such as доставать / достать.
Pulling and Crawling Out
These spatial prepositions combine naturally with more effortful verbs, such as pulling objects out (вытаскивать / вытащить) or crawling out (вылезать / вылезти).
Notice how the Genitive case remains consistent regardless of whether you are retrieving an object from behind something, or whether a creature is crawling out from underneath a piece of furniture.