arsenal has won the carling cup only twice
Technically, Arsenal have never won the Carling Cup as the League Cup has only been called that since Carling started sponsoring the competition in 2003. Arsenal have won the League Cup twice, in 1986/87 and 1992/93, when it was called the Littlewoods Cup and Coca-Cola cup respectively.
Liverpool FC have won the Carling cup six times.
Arsene Wenger has never won the Carling Cup as Arsenal manager. His team has managed to reach the final twice, losing to Chelsea and Birmingham City respectively.
Arsenal v Birmingham
Chelsea have won the League Cup 4 times, and twice as it's sponsor named "Carling" Cup.
Birmingham beat arsenal
The Carling Cup is the former name of the current Capital One Cup. Tottenham Hotspur F.C. has won this cup four times.
The Arsenal has only won the Carling Cup two times. However, English football is divided into different divisions and Arsenal is actually one of the most successful teams in English football history, winning 11 F. A. Cups for 13 total championships.