### Instruction: Simplify $\frac{8xy^2}{6x^2y}$ with $x=2$ and $y=3.$.### Response: I want to simplify this fraction by canceling out any common factors in the numerator and denominator.
I notice that both the numerator and denominator have a factor of 2, so I can divide both by 2 to get $\frac{4xy^2}{3x^2y}.$
I also notice that both the numerator and denominator have a factor of x, so I can divide both by x to get $\frac{4y^2}{3xy}.$
Finally, I see that both the numerator and denominator have a factor of y, so I can divide both by y to get $\frac{4y}{3x}.$
Now I have simplified the fraction as much as possible, and I can plug in the given values of x and y.
I get $\frac{4(3)}{3(2)} = \frac{12}{6} = 2.$