This is the 12788th most frequent Turkish word.
ittirerek
"Pushing" or "by pushing."
The word 'ittirerek' is used as a gerund to describe the manner of doing the action, specifically pushing to open the door.
Kapıyı ittirerek açtı.
He opened the door by pushing it.
Here, 'ittirerek' indicates the method used to move the chair by pushing it.
Sandalyeyi ittirerek yerine koydu.
He placed the chair back in its position by pushing it.
In this sentence, 'ittirilerek' is a passive form indicating the toy car being moved as a result of pushing.