There are many ways in which you can think a solution for the problem. Your approach should be to minimize the efforts. What if you took out one candy from the box labeled Peach and Grape?

What you have to consider is the fact that every box is labelled incorrectly. Thus if you pick a candy from the box labelled with Peach and Grape, it is evident that the box will not have a mixture of both (as it is labelled wrong). Thus you will get to know which candies are present in that box. 

Suppose the candy you take out turns out to be peach flavored, then the box labeled as Grapes is the one which contains a mixture of both peach and grapes. This is because it is labelled incorrectly and since we have already figured out the box with Peach candies, we can be confident of the fact. And then the jar labelled as peach will be the one containing grape flavored candies.

If the candy you take out from the mixed labeled box is Grape flavored, you can use the same logic to find out the rest.

Consider picking a candy from the other two boxes instead of what is told in the solution and you will find out that you will have to take out a candy from each of the boxes before being sure.