Hi Maren, 

The sentence is - 

Je ne sais pas ce que je préfère entre chercher les oœufs et les manger = I don't know what I prefer between looking for the eggs and eating them

These are two consecutive actions, looking for and eating the eggs, so you cannot use the 'gérondif' for the second one as it wouldn't make sense, you would only use it for simultaneous actions - 

J'ai appris à tricoter en regardant ma grand-mère le faire = I learned to knit by watching my grandmother do it

Hope this helps!