Question

If v = 4.00 meters/second and makes an angle of 60° with the positive direction of the y-axis, what is the magnitude of vX?

Answer 1

If I understood you correctly:
the angle between the vector and the X-axis is 30˚.
vX/v = cos(30)
Vx= v*cos(30) = 4*cos(30) = 0.617 meters/second

Answer 2

4 cos (30) = 3.46 m/s