When you combine the intermediate chemical equations, which substance do you cancel out?

In an example equation where AB + CD = AD + CB  the intermediate step would break all of the bonds before reforming them to look something like
AB + CD = A + B + C + D
A + B+ C + D = AD + CB

So combining the intermediate steps you cancel out like terms for the intermediate compounds.  If you have a specific chemical reaction I could help more.

Bis the