I chose to explain this topic because to me it is more complicated than multiplying radicals, so I think there will be more educational value for me to explain this.
The operations for adding and subtracting radicals are done with mixed radicals, so being able to convert from entire to mixed (and sometimes vise-versa) is crucial.
To be able to combine (through adding/subtracting) radicals, the index and radicand have to be the same.
As said before, we have to convert to mixed, which is done the same as before.
In mixed radical form: 
After converting to mixed, we can see that the radicals have the same index and radicand as some other radical, so now we actually add and subtract. To do this we just combine the coefficients with like terms (remember, like terms in radicals: same index & radicand)
So, 3+2 is 5, and -4-2 is -6, meaning the answer is 
In the case of operations on unsimplified mixed radicals, the mixed radical still has to be in simplest mixed radical form.
While these radicals are mixed, they still can be further simplified.
63 becomes root 7 with a coefficient of 3, but we can’t just ignore the other coefficient. to combine them, simply just multiply the coefficients. 
Do the same thing to the second radical, and you will find out that they have the same radicand in simplest forms, meaning you can further simplify.
