OK let me break this down for you step by step.
You have two bullets next to each other in a 6-barrel gun. This means there is a series of 4 chambers containing no bullets. You pull the trigger once. Nothing happens. This means that you pulled the trigger on one of the 4 empty chambers. Since the cylinder rotates only one chamber, the ONLY one of these 4 where a bullet could have rotated to the firing position is the one directly adjacent to the two bullets. If the first pull of the trigger was on any of the 3 other empty chambers, another empty chamber must rotate to the firing position - you survive.
There is therefore a 3 in 4 chance that you will survive if you pull the trigger again - 75%. If you re-spin the chambers, your chance is only 66.66%.
Can't make it much simpler than that.