Assuming you mean (2y^2 - 15y + 28) / (y - 4)
It only divides if y - 4 is a factor of 2y^2 - 15y + 28
(y - 4)(?y + ??) = 2y^2 - 15y + 28
The ? has to be 2 if we want y * 2y = 2y^2
(y - 4)(2y + ??) = 2y^2 - 15y + 28
The ?? has to be -7 if we want -4 * -7 = 28
(y - 4)(2y - 7) = 2y^2 - 15y + 28
But will it make the right middle term? FOIL to find out.
2y^2 - 7y - 8y + 28
2y^2 - 15y + 28
Yes, it works.
Now the original problem looks like:
(y - 4)(2y - 7) / (y - 4)
The y - 4's cancel, leaving us with:
2y - 7