These equations are from the college course Math 209.
Just as Philip has said, to find the answer to (f+g)(x), one simply adds [f(x)] + [g(x)] -- in this case, [-6x-1]+[4x^{2}] = -6x-1+4x^{2}, and then rearrange so the terms are in order of decreasing exponents, 4x^{2}-6x-1.
You might notice that when the problem says f+g, that's literally what we did -- we added f(x) and g(x). Similarly, (f-g)(x) would be found by
subtracting f(x)-g(x), (fg)(x) would be f(x)g(x), (f/g)(x) would be f(x)/g(x)... Order is important, mind you, (f-g)(x) is different from (g-f)(x), but basically you just do what the operator tells you to do. :)
If you have any more questions, let me know!