What is between 68 2/3 and 72 1/2 (options) 68 3/10, 747/11, 68 1/2, 550/8

Why not write all of the numbers in decimal fraction form, to make them easier to compare?

68 2/3 = 68.666 ...

72 1/2 = 72.500

68 3/10 = 68.300

74 7/11 = 74.636 ...

68 1/2 = 68.500

550/8 = 68.750

Now ask yourself: Which of the last four numbers is between 68.666 ... and 72.500?

You can do this by converting all fractions to decimal form

68 2/3 = 68.66666 ... 72 1/2 = 72.5

68 3/10 = 68.3, 747/11 = 67.909, 68 1/2 = 68.5 and 550/8 = 68.75

so we see that 68.75 (that is 550/8) is the correct option