Some good comments already, just bringing them together in the one comment :
After accepting this quest, proceed to the rooftop ( not via the stairs, as that way is blocked ). The correct way to access the terrace is by using the [object=441897] https://www.wowhead.com/object=441897/earthen-teleporteras per comment from Rapscallion001. This Teleporter is next to the Stormwind Portal down the small stairs from the quest giver ( on the left looking down the stairs).
Once on the ledge you will see a quick exchange between the two NPC's and they will proceed to fly off in the direction of Adelgonn. There is no indication at this point as to what to do.. so taking JDLKY's advice, mount up on a Dragon-Style Flying mount and off the ledge you go, but to add to that comment, if you so feel inclined ( and its what I did ) ... Have Faith !.. .I launched myself off the ledge with an old style flying mount ( Sandstone Drake ) and although it didn't "fly", as I expected it too it was gracious enough to glide a considerable distance in the air , almost to the required Adelgonn location..
Face your fear !... it requires a leap of faith..
but for those that are lacking faith, just use "jump" and it will 'regardless of old or new' flying mount use [order-advancement=2093] Vigor https://www.wowhead.com/order-advancement=2093/vigor to cast
Skyward Ascent [spell=372610]https://www.wowhead.com/spell=372610/skyward-ascent giving you a boost in the air ( point dirtecly up to maximise distance "gliding" )