First change everything to a common denominator.
So since the least common multiple of all the denominators is 16, change all the fractions to that.
To do this, multiply the existing denominators to 16, and the numerators by the same number:
For 5/8, 8 has to be multiplied by 2 to get 16, so multiply the whole fraction by 2 to get 10/16.
For 9/16, keep it bc the denominator is already 16.
For 1/4, 4 has to be multiplied by 4 to get 16, so multiply the whole fraction by 4 to get 4/16.
For 3/8, 8 has to be multiplied by 2 to get 16, so multiply the whole fraction by 2 to get 6/16.
Now put them in order: 4/16, 6/16, 9/16, and 10/16.
Now change them back to their originals by simplifying but keep them in that order: 1/4, 3/8, 9/16, 5/8