You do know what $\displaystyle J/I$ means, right? I've seen some people get stuck with this simply from not knowing what is meant by "an ideal mod an ideal".
As a set, $\displaystyle J/I=\{j+I\mid j\in J\}$. They're the cosets in $\displaystyle R/I$ whose representatives come from $\displaystyle J$. Notice that it makes sense to discuss this since $\displaystyle I\subseteq J$.