Mistborn trilogy by Brandon Sanderson fanfiction, it's the end of book 2, The Well of Ascension and Vin is teaching Elend how to be a Mistborn using the same techniques that Kelsier used with her.
Vin skidded to a halt on the mist-wetted cobbles and flared pewter for a second to steady herself, she glanced around with her tin-enhanced eyes and pouted in impatience. She adjusted her mistcloak around her and was just about to take her knives from their sheathes to check them when she heard the thump of someone landing on the ground. Turning around she saw Elend rising from a crouch and dropped a coin, propelling herself into the air before the new mistborn could take a breath. Jumping lightly over the low rooftops of the skaa apartment buildings of Luthadel she chanced a look behind her and saw Elend struggling to keep up with determination on his chiselled face. She maintained her speed and chose some more complicated routes over the rooftops to give him a proper workout until she reached the city wall and steel-pushed a belt at Elend as he continued to jump towards her. He caught the belt with a grunt and finally landed on the rooftops, his knees were shaking and his legs were weak, downing another vial of metals he began to burn pewter to make himself stronger and more focused. Strapping on the belt he noticed the big metal blocks attached at the back and looked at Vin questioningly, to which she responded by pointing off of the wall and into the mists. When he looked over the edge of the wall the mists concealed the ground, making it unknown to him how big the wall actually was other than the memories he had of travelling back to Luthadel in a carriage, taking a deep breath he dropped a coin and burned steel, watching the blue line fade as the coin got further away. He backed away two steps and took a few deep breaths, Vin, who stood about 6 feet away cleared her thoat loudly and pointed again off of the wall waiting. Shaking himself, Elend took a step forward and felt a small pair of strong hands on his back that pushed him, suddenly he was falling in the mists and flailed as he fell, completely forgetting about the coin he had dropped. The belt jerked upwards by the metal blocks as Vin concentrated on keeping him from hitting the ground and killing himself, she let him down gently and used steel to find the coin that he had dropped and leaped gracefully from the rooftop, using the coin as an anchor she hit the ground with a small thud and stood over Elend who was just about to stand up. She appeared in the corner of his vision and winked, "race you home," she said competitively and leaped right over the city wall with all the enthusiasm of a child and none of the fatigue and weariness that he felt. Elend stood up groaning, "Damn woman," he muttered under his breath before iron-pulling on a torch bracket at the top of the wall and staggered away into the mists.