I went up to 6 rpm and then tried to shift to second gear aggressively and unknowingly the clutch was not fully depressed I think and the gear change failed of course I heard the gears grinding but I also felt something stop moving in the gear knob while holding it. The car drove fine after that but how much damage did I do to the transmission?
By failing to fully disengage the clutch, you mashed the very fast spinning input shaft gears with the not as fast spinning second gear. While the synchro will have helped lessen the difference in speed, there's only so much it can do, and you probably damaged some of the teeth. Considering that the car still shifts and drives fine, I would go ahead and change your transmission fluid, and don't be surprised when you find some metal flakes in there. You should also make sure you have a magnetic drain bolt, which will help collect any metal shavings that break off when miss-shifts occur.
I don't know what your car model and year are but most modern vehicles have what is called a rev limiter.
Rev limiters are typically electric in nature and cut out the ignition spark on cylinders when the RPM's exceed the manufacturers max limit on the engine.
This prevents the engine from getting damage due to excessive RPM's.
IF (and I know you didn't) you went from 4th gear to 2nd at 70mph, or something like this, the rev limiter would do you know good because you engine RPM's would not be controlled by combustion at that time. They would be controlled by the rotation of the tires and a direct connection to your engine via the transmission.
I have seen young people put their foot on the gas and take it to the floor in neutral and just run their engine against the rev limiter a few times, just to make the noise. I will say this isn't good for you car and I don't recommend doing it.
You have a safety mechanism that prevents damage to your vehicle when you encounter a situation like you did. Missing a shift won't hurt a modern vehicle with a rev limiter. You should have nothing to worry about.