I checked our record in the 6th round.
City 21/22 - lost
Bournemouth 20/21 - won
Wigan 17/18 - won
United 04/05 - lost
Wolves 02/03 - won
United 95/96 - lost
Norwich 91/92 - lost replay
Brighton 85/86 - won
Sheffield Wednesday 83/84 - won replay
Arsenal 78/79 - lost replay
Bradford 75/76 - won
Forest 62/63 - won second replay
Spurs 47/48 - lost
7 wins 6 losses
There were some earlier “quarter final” appearances but they weren’t 6th round proper, all wins though, 5 of them.