“Pantea's Flute” is a Bards College Faction Quest in The Elder Scrolls V: Skyrim
After you have joined the Bards College you can talk with Pantea Ateia to get this quest. She will explain that her student Larina took her flute and sold it to some Necromancer. Pantea only knows because the Necromancer sent a ransom note! The Necromancer is apparently hiding out in Hob's Fall Cave. She wants you to head there and retrieve the Flute from the Necromancer. She will send you there to retrieve her Flute.
To reach Hob's Fall Cave, either head East from Dawnstar or West from Winterhold along the shore.
Once inside, head to the North into the first room with all the cages. Go forward then turn to the West. Follow the passage as its meanders to the North. You are likely to encounter a Skeleton just after the turn. Follow the passage as it turns back to the West.
You will come to a small chamber before too long. In it you will encounter a Novice Necromancer. They will come out after you and attack. Be wary that they can raise some undead against you. Defeat them, search the small chamber for Soul Gems, potions and books. After that, follow the passage as it winds to the South.
Continue around the corners. The passage will turn to the North. You will encounter more Skeletons and an Ascendant Necromancer. Deal with them and then continue forward. This will lead to a room with a bridge going across it. On the far side is another Necromancer and skeleton. Take them out at a distance or charge in quickly at your preferred time. Head across the bridge to progress. You will find another Necromancer just around the corner.
The next few turns allow you to reach another chamber. Inside it is a pair of Necromancers and a number of Skeletons. If you are having trouble with this fight, pull back into the hallway you entered through. Take your time with the fight and win it.
Inside the room you will find an Arcane Enchanter on the Southern wall that you can use. It also has the skill book: Enchanter's Primer.. The door forward through is closed. There is a locked chest (Apprentice Level) on the Northern side of the room that can be opened.
To exit, head over to the Eastern side. To the right of the gate is a [pull chain. Interact with it to lower the gate. Head on through it.
Be careful as you round the corner. There are 4 small sconces set up with Soul Gems in them. They are set up to cast a spell when someone passes by them. Approach them from a side and take the Soul Gem. This deactivates the trap that the Soul Gems create. With the spell disabled, continue forward to the South. Along the passage you will find another Necromancer patrolling the area. Take them out to continue forward.
This leads to a multi-level chamber with 3 more Necromancers. The divides in the area allow you to more more easily sneak around to get in good positions if you play that way. The Necromancers are on the top floor, giving them something of an advantage. if you attack from the entrance to the room from the corridor, this will draw them down and out.
Make your way up to the top level after you have dealt with the Necromancers. On the Northern wall you will find the loot chest. Open it up to find Pantea's Flute and more treasure. On the nearby table you will find the corpse of Larina.
To exit the dungeon quickly, head to the Southwest. You will see a pair of suspended cages. Head between them and drop down. It is a quick trip now to exit out of the dungeon.
Return to the Bards College. Talk with Pantea Ateia. She will reward you with +1 to Alteration, Conjuration, Destruction, Enchanting, Illusion and Restoration