So in episode 4x7(Cops & Robbers) in the end 城 発言しました that he has saved Beckett 9 times and she has saved him 8 time. Can someone write all the times? I counted in my head and i didn't get so many.

Well this kind off depends on what one would define as saving, But I got a 一覧 which I think would be the 9 saves for 城 and the 8 for Beckett:)

Beckett:

Season 1: Episode 7 saves him from a guy that hits him and tries to shoot him

Season 2: Episode 1 saved him from a Russian gunman

Episode 13 saves him from her mothers killer

Episode 19 saves 城 from the curse

Season 3:

Episode 6 saves him from the 3xk in the hotel room

Episode 16 got him out of the room of radiation

Season 4 : Beckett: Saves 城 in the bank


Castle:

Season 1: Episode 6 saves Beckett from a gun shooting man

Season 2: Episode 17 saves her from the bomb in the apartment

Episode 18 he shoots the gun out of the killers hand when he tries to shoot Beckett

Season 3: Episode 1 saved her from a gunshot

Episode 13 he beats up a guy that is going to shoot her

Episode 17 he held her in the cold so they survived.

Season finale saved her twice: first with Montgomery in the hangar, then at Montgomerys funeral

Mutual thing :
Shooting people holding 銃 behind them season 3 episode 1