Iused the answer key to get my answer and checked it with my dumb useless teacher and it’s right but, he won’t tell me how to get the numerators like how does it go from 3 & 7 to 15 & 14

You multiply it with the same number you use for the denominator.
in this case 3/4 and 7/10
you find the LCM of the denominator is 20
so for 4 to become 20 you multiply by 5 then for the numerator 3 also multiply by 5, so you get 15/20
its the same also with 7/10, you multiply both the numerator and the denominator by 2 and get 14/20
hope it help... :)