I see the light moving exactly at speed equal to c.
In fact, the second postulate of special relativity states that:
"The speed of light in free space has the same value c in all inertial frames of reference."
The problem says that I am moving at speed 2/3 c, so my motion is a uniform motion (constant speed). This means I am in an inertial frame of reference, so the speed of light in this frame must be equal to c.
