Ok here we go. This is going to be extremely painful to explain so let's start slowly with relativity's point of view.
Here is light speed from Bob's perspective. In relativity, there are no units for light but I'm going to introduce them anyway. From Bob's perspective, light travels one of his distance units (a Bob light year) in one of his time units (a Bob year).
Now we add Alice's Minkowski coordinate frame at 6c.
In relativity, Alice's coordinates are not square cartesian but rhombic Minkowski. At first glance it looks like both frames share the same light line. Alice's perspective of the light line in her frame is she travels one of her distance units (an Alice light year) in one of her time units (an Alice year). But hold on, Alice's perspective of the light line is it travels 2 Bob light years in one Alice year.
An Alice year from Bob's perspective is 1.25 Bob years. An Alice year is also .8 Bob yrs from Alice's perspective.
Which means from Bob's perspective of the speed of light through Alice's frame using Bob's units is 2 Bob ly/1.25 Bob yrs =1.6c.
Bob's perspective of the speed of light through Bob's frame using Bob's units is only 1 Bob ly/1 Bob yr = 1c.
Alice's perspective of the speed of light through Alice's frame using Alice units is 1 Alice ly/1 Alice yr = 1c.
Alice's perspective of the speed of light through Alice's frame using Bob units is 1.25 Bob ly/1.25 Bob yr = 1c.
Alice's perspective of the speed of light through Bob's frame using Bob units is 2 Bob ly/.8 Bob yr = 2.5c.
The permutations of perspective, mixed perspective and units go on and on. What's important here is if you consider each frame as independent, there is no confusion that each one sees his velocity through space is 0c, his velocity through time is 1c and the velocity of light through his space is 1c (light has no velocity through time, it's all through space). All the difficult interpretation happens when 1 frame tries to include another frame into his perspective of his own frame.
So now we're going to use ralfativity to clear things up. First, the formula for light units is:
c'=Rc where R is the doppler shift ratio (2 @.6c, 3 @.8c).
c' is the velocity of light Bob sees from his perspective through Alice's frame using her time units t' and Bob's space units x.
Here's an example:
In it Alice travels 3 Bob light years to some planet in 4 of her years. How long did it take light from her starting point on earth to reach the same planet from Bob's perspective through her frame using her units t' and Bob's space units x?
Bob's space units = 3 Bob ly purple line
Her time units in her frame = 1.5 Alice yrs green line
So c' in this mixed perspective = 2c
In ralfativity Alice travels at v' which is Yv which is x/t'. Bob's perspective of her is .75c and light being no different than any other velocity, he sees c at c' which is 2c. All this is because of the pre-agreed distance markers that were set up around earth's stationary reference frame.
There's a difference between reality and perspective in ralfativity, that distinction is not made in relativity. This is the reality Bob sees from his perspective:
When Alice reaches the planet, she has aged 4 yrs through time (which appears on her clock readout) and 1 year through space for a total ralfativistic age of 5. Bob has also aged 5 years in the instantaneous present when Alice touches the planet. Since it's his perspective and he hasn't moved, the clock readout on his clock is all age, none is lost to distance.
From Bob's relativistic perspective, light would take 3 Bob yrs to travel that distance (3 Bob ly) and Alice 5 Bob yrs at .6c. From Bob's ralfativistic perspective, light only takes 1.5 Alice years to travel 3 Bob ly and Alice 4 Alice years at .75 c. The distances inside Alice's ship are the same distances outside her ship. Space is invariant in ralfativity and v' and c' are not subject to the rules of v and c.
I figure it'll take about 20 re-reads before the questions stop about why my knobs max out at 10 and relativity's are set to 11. An intelligent question would be how ralfativity handles the train and the train station example if the train doesn't length contract from the station's perspective (and vice versa). Nessun dorma!