How many moles of liquid water must freeze to remove 100 kj of heat? (δhf = –334 j/
g.

First figure out how many grams must freeze and then convert the grams to moles. 
Hf = -334 J/g. Convert this to KJ/g by dividing by 1000. (There are 1000 Joules in a kJ). 
Hf = -334 J/g ÷ 1000 J/kj = -0.334 kJ/g 
Now, divide 100 kJ by -0.334 kJ/g (see how the units are lining up?) 
100 kJ ÷ -0.334 kJ/g = 299 g 
Now convert this to moles by dividing by the molecular weight of water (18.0g/mole). 
299 ÷ 18.0 = 16.6 moles