This is the 14482nd most frequent Polish word.
przesunięciu
"Przesunięciu" means "shift" or "displacement" (in the dative or locative case).
Here, 'przesunięciu' is used as a noun in the locative case referring to the act of delaying or rescheduling.
Przesunięciu terminu spotkania pomogło nam lepiej zaplanować nasz czas.
The rescheduling of the meeting helped us better plan our time.
In this sentence, 'przesunięciu' is used to describe the action of moving the picture in locative case.
Przesunięciu obrazu na ścianie towarzyszyło lekkie skrzypienie.
The shifting of the picture on the wall was accompanied by a slight creak.
'Przesunięciu' in this context denotes the action of moving something, again in locative case, following a preposition.