She followed the doctors advice because she trusted him.
a. the doctors' advice
b. the doctor's advice
c. the doctors's advice
choose the response below that demonstrates the correct form of contraction for the words below. you are
a. you're
b. your

The question is about the advice that belongs to the doctor. The apostrophe is used to show possession. Since there is only one doctor involved, the apostrophe appears after the r. 
The answer is: 
a. the doctor's advice

There are two spellings of the word "your", each with a different meaning. One is about possession; eg. "it is your fault, not mine!" 
The other is a shortened version of "you are". The "re" at the end of "you're" is the end of the "are". That is the clue as to what it means. 
The answer is: 
a. you're