What quest do you mean? Is this the one with the A-Class Mount Card?
To do that quest, you should click on the ‘Rewards Hall’ button, then click on the Level Pack’ tab. This should allow you to collect an A-Class Mount Card from the level 10 rewards, and if you use that card then you will be able to select a mount to complete the quest.
That quest is presented in a slightly confusing way, so a few people have had problems with it. However, if you had problem with some other level 10 quest, then please give details about what the quest was and what the problem with it was.