[g_orbital]

I have found a reaction which converts 1,4-dimethoxybenzene derivative into the benzoquinone derivative, by two different synthetic methods: The one uses CAN (ammonium cerium nitrate), CH₃CN-H₂O. The other one makes use of AgO + HNO₃ in dioxane.

What's the mechanism of this conversion in each method?

Thank you very much indeed!

[movies]

Where did you come across this?  A guy in my lab recently finished a synthesis of that molecule as well.

As to your question, both of those reagents likely function through sequential one-electron oxidations wherein an electron is  "pulled out" of the electron rich aromatic system in the substrate and onto your oxidizing agent.  Eventually the methyl groups fall off, probably via S_N2 attack by water.