It takes 8 hours for three identical water pumps to fill up a pool. How long would it take four of the same pumps to fill up the same pool?
If three identical water pumps can fill up the pool in 8 hours, then one pump would take 3 times longer, or 24 hours, to fill up the pool alone.
Therefore, if there are four of the same pumps working together, it would take one-fourth of the time to fill up the pool.
Hence, it would take 24 hours/4 = <<24/4=6>>6 hours for four identical water pumps to fill up the pool. Answer: \boxed{6}.