She bought 3 1/2 yards
make it all in fraction:
(3*2 + 1)/2 = 7/2
if she used 2/3 of that that means she left 1/3 of it
1/3 of something is 1/3 times that:
1/3* 7/2 = 7/6
since numerator is greater than denominator we have at least 1 whole yard there.
7-6 = 1 < 6 which means we have 1 whole yard
Answer is 1 1/6 yards