Question

Do 1/3 and 2/6 name the same part of one whole?

Answer 1

Yes because 1/3 and 2/6 are the same. For example:
2/4 and 1/2 are the same because 2/4 can be reduced down to 1/2. In your equation 2/6 can be reduced to 1/2. Therefore 2/6 = 1/3

Answer 2

Yes, if you were to divide 1/3 you would get 1/6. 
Now since you divided 1/3 into two parts to get 1/6, now if you would like to get 1/3 out then you must double 1/6 into 2/6 which would be equal to 1/3

I hope this made sense, I know you wanted a more simple yes or no but i believe if you explain to someone how they got the answer than you wouldn't need help next time. xx