This is the 10965th most frequent Russian word.
вытащить
"To pull out" or "to extract."
The verb 'вытащить' is used here to mean removing or pulling an item (the book) from a confined space (under the cabinet).
Я смог вытащить книгу из-под шкафа.
I managed to pull the book out from under the cabinet.
Here, 'вытащить' means to retrieve something (the curtains) from an enclosed or immersive situation (the wash).
Можешь вытащить занавески из стирки?
Can you take the curtains out of the wash?
In this figurative usage, 'вытащить' refers to helping someone escape or be relieved from a challenging or metaphorically confining circumstance (a difficult situation).