Infection - as in germs
Infestation - as in lice
I don't know what training course you are doing, but check the words in a dictionary as they mean different things.
The 'cross' word in this instance would mean - transferring from one to another.
So cleaning & sanitising of work areas, tools & implements would kill germs & remove lice/nits eggs from combs & brushes.
Try putting the words into Google and see what comes up.
I'm not a hairdresser, but I'm sure I'm on the right track here - although you'd need to word it correctly.