The end of answer C is correct, and the end of B is not, since it changes the meaning. This is a bit of a subtle point, but if you look at B, it says:
"allowing the skin time to build a protective layer and to fight the radiation"
which, inserting the implied words, means:
"allowing the skin time to build a protective layer, and allowing the skin time to fight the radiation"
But the skin doesn't need to be allowed time to fight the radiation -- the skin needs the protective layer, and that layer will fight the radiation. C gets that meaning across:
"allowing the skin time to build a protective layer to fight the radiation"
which, inserting the implied words, should be read to mean:
"allowing the skin time to build a protective layer in order to fight the radiation"
which conveys the intended meaning correctly. Incidentally, we use the word 'to' in this way a lot, as a shorthand for 'in order to': "to improve your GMAT score, you should do practice problems" really means "in order to improve your GMAT score, you should do practice problems".
And the final perplexing thing about this question is the beginning: "Dr. Steven suggests drinking warm cold water " -- what is "warm cold water"?