First, let's find a common denominator to more easily compare the fractions.
12 will work just fine.
5/6 becomes 10/12, because 6x2=12, and 5x2=10
1/4 becomes 3/12, because 4x3=12, and 1x3=3
2/3 becomes 8/12, because 3x4=12, and 2x4=8
Now, we add them together, two at a time, to find the pieces that will make a length at least one yard, and closest to one yard.
10/12+3/12=13/12 This is 1/12 more than 1 yard.
10/12+8/12=18/12 This is 6/12 more than 1 yard.
8/12+3/12=11/12 This is 1/12 less than 1 yard.
The two pieces that will make a length of at least 1 yard, and are closest to 1 yard are the 5/6 (10/12) yard and 1/4 (3/12) yard pieces.
If Carl uses the two shortest pieces, the 1/4 (3/12) yard and 2/3 (8/12) yard pieces, he will need 1/12 more cable.
3/12+8/12=11/12
12/12-11/12=1/12