The X & the C don't start at the yard.
They begin the route from a lay-up track which is different. The yard for the C is Pitkin Yard which is all the way in Brooklyn/Queens right after Grant Avenue.
Like the R Shuttle and the F train routes. Right after you finished the run you place the trainset onto a lay-up track.
On the F, right after 179 st, and the R after 36, you place the train on a layup track, not in the yard.
Heres an example of what a train yard looks like.
What YankeesPwnMets mean is to start the route from the yard itself and move on to the destination
As you see in the video the train moves out of Coney Island Yard which is just near the Ave. X station
Actually, there IS a yard just north of 168th street, the 174th street yard. It is underground, and is used to store the (C) trains, so technically the (C) line does start from a yard. The Pitkin yard is mainly used to store the (A) trains, not the (C)