A teacher did this problem with us in class but I dontn get it please explain.

2xy + 6
-------
3y + 4x

x = 2
y = 6

answer 3

please explain!

The way you typed it ....

(2xy + 6)/(3y+4x) , for x=2, y=6
=(2(2)(6) + 6) / (3(6) + 4(2))
= (24+6)/(18+8)
= 30/26
= 15/13

So clearly that is not the way the question was phrased.
PLease retype it, using brackets.