4x^4y - 8x^6y^2 + 12x^8y^6 / 4x^4y
First, look at the numbers that aren't exponents. On top we have 4, 8, and 12. On the bottom we have 4. We can cancel 4's out of everything giving us this:
x^4y - 2x^6y^2 + 3x^8y^6 / x^4y
Next, look at the x's. On top we have x^4, x^6, and x^8. On the bottom we have x^4. We can cancel an x^4 out of everything giving us this:
y - 2x^2y^2 + 3x^4y^6 / y
There's a y in everything, so we can cancel out a y, giving us this:
1 - 2x^2y + 3x^4y^5
That's it. That's the answer.