All the gummy machines at a candy factory work at the same rate and currently, six machines that working simultaneously are completing a big order in 22 hours. How many hours would it take to finish the order if the number of working machines increased by a factor of 4?
If currently, six machines are completing the order in 22 hours while operating simultaneously, the rate of one machine is 1/6 of the order per 22 hours.
To complete the whole order, each machine fills (1/6)/(22) = 1/(6*22) of the order's gummies per hour.
If we increase the number of machines by a factor of 4, the total number of machines is 4*6 = <<4*6=24>>24.
If 24 machines work simultaneously, they complete the gummy production at a rate of 24*(1/(6*22)) = 1/11 order's worth of gummies per hour.
Therefore, it would take the machines working simultaneously 11 hours to complete the full order. Answer: \boxed{11}.