It takes three copies of 1/6 to show the same amount as one copy of 1/2.
Why this is is because a sixth is smaller than a half. There are six sixths in a whole. There are only two halves in a whole.
So when you divide the whole into six parts, you would need half of the parts to have a half. Like down here: (not correct to scale, sorry)
|-------------------|----------------------|
|-----|------|-------|------|-------|-------|
It takes 3 of the sixths to = 1 half.
another way you can check is by simplifying your fractions.
3/6, when you divide by 3 top and bottom, = 1/2
I hope this answers your question somewhat. Please ask if there's anything more