You need to convert from gallons/second to milliliters/hour. You can do this using a series of conversion factors to go from gallons to milliliters and from seconds to hours. A conversion factor gives the relationship between two units. Start with the given quantity, and multiply it by conversion factors so that the units you've started with cancel out and you're left with the units you want. This method is called dimensional analysis.
You'll need conversion factors that tell you how many milliliters are in a gallon and how many seconds are in an hour. You can use conversion factors that give intermediate steps, for example I know that There are 3.8 liters in a gallon and 1000 milliliters in a liter, so I'll use two conversion factors to convert from gallons to milliliters. Likewise, I'll use two factors to convert from seconds to hours:
37 gallons/second x (3.8 liters/gallon) x (1000 ml/liter) x
(60 seconds/1 minute) x (60 minutes/1 hour)
= (37)(3.8)(1000)(60)(60) milliliters/hour = 5.06 x 10^8 ml/hour
Gallons, liters, seconds and minutes all canceled out to leave ml/hour.
Every conversion factor has a reciprocal that used for the opposite operation. If I was converting from liters to gallons I'd use (1 gallon/3.8 liters) so that liters would cancel out and I'd end up with gallons.