For these 'functions' questions, you just plug in the value. So, in the table it would be:
a)
x = -2, f(x) = 4(-2) + 24 = 16, g(x) = 2^(-2 + 6) = 2^4 = 16.
x = -1, f(x) = 4(-1) + 24 = 20, g(x) = 2^(-1 + 6) = 2^5 = 32
x = 0, f(x) = 4(0) + 24 = 2, g(x) = 2^(0 + 6) = 64.
b) The solution, based on the table, is x = -2.
c) Because the 'solution' of two functions is when the two function's lines (graphs) intersect. In algebraic form, this is when the two function's output is the exact same. The output is the same when x = -2 and so, that's the solution to the system of functions.