You are just solving the derivatives like normal but it is written in a strange way that may seem confusing at the first time.
For a) for instance, imagine f(x) to be x^2 and g(x) to be x
therefore h(x) = x^2 + x right? when you take the derivative of h(x) you take the derivative of each term.... so in my made up example h'(x) = 2x + 1 right?
The examples given are exactly the same. h(x) = f(x) + g(x) so..........
h'(x) = f'(x) + g'(x)
After that you can finally use the information given;
h'(4) = f'(4) + g'(4), and from the table you know those two values, so
h'(4) = 3 + (-2) = 1
Simply follow these steps and basic derivative steps to solve b) and c)