How snap object to X, Y or Z-axis? I am a Blender n00b and have this beginners question that I can't find an answer for.

I'm following this course by testedpancake on YouTube to model a car. In part 7 of his tutorial he is extruding the hood of the car to the Y-axis: 
Model a 3d Car | part 7 | hood vents and topology examples

In my case I cannot get one point of the edge that I want to align with the Y-axis to snap to it. Please see the pictures below.

When I zoom in the vertice is not attached to the Y-axis

My question: how do I snap a vertice to the Y-axis?

Can somebody please help me out? Thank you!

EDIT: Here's the file: Dodge Challenger car

Selecting the edge to move to Y-axis


Having 2 points snapped to the Y-axis, but not really!


When I zoom in, the vertice is not aligned with the green Y-axis at all!
Enable clipping in the mirror modifier and then try again. If you now move your vertices to the left they should stop when they touch the other mirrored vertices.