I'm not sure what to do after this, but can you please answer the problem with the method I used I get confused with using other methods.

we have the expression
[tex]\frac{3y+2}{3y}\colon\frac{6y^2+4y}{3y+2}[/tex]step 1
Simplify the second term
so
[tex]\begin{gathered} \frac{3y+2}{3y}\colon\frac{2y(3y+2)}{3y+2} \\ \\ \frac{3y+2}{3y}\colon2y \end{gathered}[/tex]step 2
Multiply in cross
[tex]\frac{(3y+2)}{3y\cdot2y}[/tex][tex]\frac{(3y+2)}{6y^2}=\frac{1}{2y}+\frac{1}{3y^2}[/tex]