Are the following expressions equivalent? show work.

3xy^2 / 4y and 6xy^2 / 8xy

No, they are not. When they are simplified to find if they are equivalent or not, the numerator can be divided out like so:

3xy (3xy)             6xy (6xy)
           
    4y                        8xy

Then the cross-cancel method can be used to simplify the two fractions, which later simplifies to:

3x (3xy)                3 (6xy)
               
     4                           4

Hence, they are not equivalent to each other.