To complete the Vahtacen's Secret quest in The Elder Scrolls IV: Oblivion , follow these steps:

Starting the Quest

• Finish the previous Mages Guild quest Ulterior Motives and reach the rank of Evoker.
• Speak to Raminus Polus at the Arcane University to receive the quest.
• Then talk to Irlav Jarol , also at the Arcane University, who will send you to the Ayleid ruins of Vahtacen, located south of Cheydinhal

At Vahtacen

• Enter the ruins and speak with Skaleel , who will mention a mysterious pillar blocking progress.
• Use the Vahtacen Key (given by Irlav) to open a locked door and proceed deeper into the ruins.
• Find Denel , a mage researching the pillar, who will tell you the pillar reacts to magic but requires a specific spell sequence to open

Solving the Pillar Puzzle

• Read the inscriptions on the four tablets in the corners of the pillar room. Denel will translate them after you get a reference manual from Skaleel.
• The tablets correspond to the following magical effects:
  • "Av Molag Anyammis" - Fire spells (Life)
  • "Av Mafre Nagala" - Frost spells (Death)
  • "Magicka Loria" - Damage Magicka (Darkens)
  • "Magicka Sila" - Fortify Magicka (Shines)

• You need to cast the following single-effect spells on the pillar in this exact order:
  1. Flare (fire spell)
  2. Snowball (frost spell)
  3. Sever Magicka (damage magicka spell)
  4. Elevate Magicka (fortify magicka spell)
• Stand close to the pillar and cast each spell carefully. Casting the wrong spell will cause a lightning bolt to strike you.
• If you don’t have the spells, you can find scrolls of these spells in a chest near Denel or buy them from Mage's Guild merchants

After the Puzzle

• Once the pillar moves and reveals a path, proceed to retrieve the Ancient Elven Helm.
• Return to Skaleel and then back to Irlav Jarol to complete the quest.
• Finally, report back to Raminus Polus to receive your promotion to Conjurer and the Robe of the Conjurer as rewards

This quest is notable for its puzzle involving casting spells in a precise order on a magical pillar to unlock further progress in the ruins. Following the above steps will help you solve it efficiently.