If Tina's pail holds 4 gallons and Tommy's holds 2 more gallons than hers, that means Tommy's holds 4+2=<<4+2=6>>6 gallons.
If Timmy's pail holds twice as much as Tommy's 6-gallon pail, that means it holds 6*2=<<6*2=12>>12 gallons.
Therefore, in 1 trip that means all three move a total of 4+6+12=<<4+6+12=22>>22 gallons.
In three trips, that means they would move a total of 22*3=<<22*3=66>>66 gallons
#### 66