If we multiply each by 4/3, we can look to see which is closest to 1. This step is not strictly necessary, but it is often easier to compare to 1 than to compare to 0.75.)
30/42*4/3 ≈ .95238 (differs from 1 by .04762)
15/19*4/3 ≈ 1.05263 (differs from 1 by .05263)
45/63*4/3 ≈ .95238 (this is an equivalent to the first fraction)
39/51*4/3 ≈ 1.01961 (differs from 1 by .01961)
63/86*4/3 ≈ .97674 (differs from 1 by .02326)
The closest value to 3/4 is 39/51 = 13/17
30/42*4/3 ≈ .95238 (differs from 1 by .04762)
15/19*4/3 ≈ 1.05263 (differs from 1 by .05263)
45/63*4/3 ≈ .95238 (this is an equivalent to the first fraction)
39/51*4/3 ≈ 1.01961 (differs from 1 by .01961)
63/86*4/3 ≈ .97674 (differs from 1 by .02326)
The closest value to 3/4 is 39/51 = 13/17