Alright, here’s the quick truth — for two photons approaching each other, their relative velocity (by special relativity) is c, not 2c.  

It feels weird because in everyday life we’d just add the speeds, but for light, no matter whether they’re moving toward or away, the “relative speed” you calculate from relativity’s velocity addition formula maxes out at c. Light just doesn’t get any faster than itself.  

You want me to show you exactly how plugging into the formula makes that 2c idea vanish? It’s pretty neat.